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#include <multi_domain_linearised_axisym_navier_stokes_elements.h>

Inheritance diagram for RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement:

Public Member Functions
	RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement ()
	Constructor: call the underlying constructors. More...

virtual void	get_base_flow_u (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &result) const
	Overload get_base_flow_u(...) to return the external element's velocity components at the integration point. More...

virtual void	get_base_flow_dudx (const double &time, const unsigned &ipt, const Vector< double > &x, DenseMatrix< double > &result) const
	Overload get_base_flow_dudx(...) to return the derivatives of the external element's velocity components w.r.t. global coordinates at the integration point. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute the element's residual vector and the Jacobian matrix. More...

Public Member Functions inherited from oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement
	RefineableLinearisedAxisymmetricQCrouzeixRaviartElement ()
	Constructor. More...

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 6 (velocities) More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: Reconstruct pressure from the (merged) sons. More...

unsigned	nrecovery_order ()
	Order of recovery shape functions for Z2 error estimation: Same order as shape functions. More...

unsigned	nvertex_node () const
	Number of vertex nodes in the element. More...

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)
	Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here. More...

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)
	Get all function values [U^C,U^S,...,P^S] at previous timestep t (t=0: present; t>0: previous timestep). Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here. Note: No pressure history is kept, so pressure is always the current value. More...

void	further_setup_hanging_nodes ()
	Perform additional hanging node procedures for variables that are not interpolated by all nodes. Empty. More...

void	further_build ()
	Further build for Crouzeix_Raviart interpolates the internal pressure dofs from father element: Make sure pressure values and dp/ds agree between fathers and sons at the midpoints of the son elements. More...

Public Member Functions inherited from oomph::LinearisedAxisymmetricQCrouzeixRaviartElement
	LinearisedAxisymmetricQCrouzeixRaviartElement ()
	Constructor: there are three internal values for each of the two pressure components. More...

virtual unsigned	required_nvalue (const unsigned &n) const
	Return number of values (pinned or dofs) required at local node n. More...

double	p_linearised_axi_nst (const unsigned &i_internal, const unsigned &i) const
	Return the pressure value i at internal dof i_internal (Discontinous pressure interpolation – no need to cater for hanging nodes) More...

unsigned	npres_linearised_axi_nst () const
	Return number of pressure values corresponding to a single pressure component. More...

void	fix_pressure (const unsigned &p_dof, const double &pvalue)
	Fix both components of the internal pressure degrees of freedom p_dof to pvalue. More...

int	p_local_eqn (const unsigned &n, const unsigned &i)
	Overload the access function for the i-th component of the pressure's local equation numbers. More...

void	output (std::ostream &outfile)
	Redirect output to NavierStokesEquations output. More...

void	output (std::ostream &outfile, const unsigned &n_plot)
	Redirect output to NavierStokesEquations output. More...

void	output (FILE *file_pt)
	Redirect output to NavierStokesEquations output. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	Redirect output to NavierStokesEquations output. More...

unsigned	ndof_types () const
	The number of "dof-blocks" that degrees of freedom in this element are sub-divided into: Velocity and pressure. More...

Public Member Functions inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
	LinearisedAxisymmetricNavierStokesEquations ()
	Constructor: NULL the base flow solution and the derivatives of the base flow function. More...

const double &	re () const
	Reynolds number. More...

const double &	re_st () const
	Product of Reynolds and Strouhal number (=Womersley number) More...

const int &	azimuthal_mode_number () const
	Azimuthal mode number k in e^ik(theta) decomposition. More...

double *&	re_pt ()
	Pointer to Reynolds number. More...

double *&	re_st_pt ()
	Pointer to product of Reynolds and Strouhal number (=Womersley number) More...

int *&	azimuthal_mode_number_pt ()
	Pointer to azimuthal mode number k in e^ik(theta) decomposition. More...

const double &	viscosity_ratio () const
	Viscosity ratio for element: element's viscosity relative to the viscosity used in the definition of the Reynolds number. More...

double *&	viscosity_ratio_pt ()
	Pointer to the viscosity ratio. More...

const double &	density_ratio () const
	Density ratio for element: element's density relative to the viscosity used in the definition of the Reynolds number. More...

double *&	density_ratio_pt ()
	Pointer to the density ratio. More...

virtual unsigned	u_index_linearised_axi_nst (const unsigned &i) const
	Return the index at which the i-th unknown velocity component is stored. The default value, i, is appropriate for single-physics problems. In derived multi-physics elements, this function should be overloaded to reflect the chosen storage scheme. Note that these equations require that the unknowns are always stored at the same indices at each node. More...

double	du_dt_linearised_axi_nst (const unsigned &n, const unsigned &i) const
	Return the i-th component of du/dt at local node n. Uses suitably interpolated value for hanging nodes. More...

void	disable_ALE ()
	Disable ALE, i.e. assert the mesh is not moving – you do this at your own risk! More...

void	enable_ALE ()
	(Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. Note: By default, ALE is enabled, at the expense of possibly creating unnecessary work in problems where the mesh is, in fact, stationary. More...

virtual int	p_index_linearised_axi_nst (const unsigned &i) const
	Which nodal value represents the pressure? More...

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
	Strain-rate tensor: $e_{ij}$ where $i,j = r,z,\theta$ (in that order) More...

void	output_veloc (std::ostream &outfile, const unsigned &nplot, const unsigned &t)
	Output function: r, z, U^C, U^S, V^C, V^S, W^C, W^S, in tecplot format. nplot points in each coordinate direction at timestep t (t=0: present; t>0: previous timestep) More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Compute the element's residual Vector. More...

void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Add the element's contribution to its residuals vector, jacobian matrix and mass matrix. More...

double	interpolated_u_linearised_axi_nst (const Vector< double > &s, const unsigned &i) const
	Return the i-th component of the FE interpolated velocity u[i] at local coordinate s. More...

double	interpolated_p_linearised_axi_nst (const Vector< double > &s, const unsigned &i) const
	Return the i-th component of the FE interpolated pressure p[i] at local coordinate s. More...

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)
	Set the dimension of the element and initially set the dimension of the nodes to be the same as the dimension of the element. More...

void	set_nodal_dimension (const unsigned &nodal_dim)
	Set the dimension of the nodes in the element. This will typically only be required when constructing FaceElements or in beam and shell type elements where a lower dimensional surface is embedded in a higher dimensional space. More...

void	set_nnodal_position_type (const unsigned &nposition_type)
	Set the number of types required to interpolate the coordinate. More...

void	set_n_node (const unsigned &n)
	Set the number of nodes in the element to n, by resizing the storage for pointers to the Node objects. More...

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const
	Return the local equation number corresponding to the i-th value at the n-th local node. More...

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const
	Compute the geometric shape functions (psi) at integration point ipt. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of "detJ" w.r.t. the nodal coordinates. More...

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()
	The destructor cleans up the static memory allocated for shape function storage. Internal and external data get wiped by the GeneralisedElement destructor; nodes get killed in mesh destructor. More...

	FiniteElement (const FiniteElement &)=delete
	Broken copy constructor. More...

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const
	Compute centre of gravity of all nodes and radius of node that is furthest from it. Used to assess approximately if a point is likely to be contained with an element in locate_zeta-like operations. More...

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Get local coordinates of node j in the element; vector sets its own size (broken virtual) More...

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of the node j in the element A dumb, but correct default implementation is provided. More...

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)
	Get the local fraction of any node in the n-th position in a one dimensional expansion along the i-th local coordinate. More...

MacroElement *	macro_elem_pt ()
	Access function to pointer to macro element. More...

void	get_x (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates. Either via FE representation or via macro-element (if Macro_elem_pt!=0) More...

void	get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). Either via FE representation of QElement or via macro-element (if Macro_elem_pt!=0). More...

virtual void	set_integration_scheme (Integral *const &integral_pt)
	Set the spatial integration scheme. More...

Integral *const &	integral_pt () const
	Return the pointer to the integration scheme (const version) More...

virtual void	shape (const Vector< double > &s, Shape &psi) const =0
	Calculate the geometric shape functions at local coordinate s. This function must be overloaded for each specific geometric element. More...

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const
	Return the geometric shape function at the ipt-th integration point. More...

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Function to compute the geometric shape functions and derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element. (Broken virtual function — specifies the interface) More...

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const
	Return the geometric shape function and its derivative w.r.t. the local coordinates at the ipt-th integration point. More...

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Function to compute the geometric shape functions and also first and second derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element (if required). (Broken virtual function — specifies the interface). Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Return the geometric shape function and its first and second derivatives w.r.t. the local coordinates at the ipt-th integration point. Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual double	J_eulerian (const Vector< double > &s) const
	Return the Jacobian of mapping from local to global coordinates at local position s. More...

virtual double	J_eulerian_at_knot (const unsigned &ipt) const
	Return the Jacobian of the mapping from local to global coordinates at the ipt-th integration point. More...

void	check_J_eulerian_at_knots (bool &passed) const
	Check that Jacobian of mapping between local and Eulerian coordinates at all integration points is positive. More...

void	check_jacobian (const double &jacobian) const
	Helper function used to check for singular or negative Jacobians in the transform from local to global or Lagrangian coordinates. More...

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const
	Compute the geometric shape functions and also first derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const
	Return the geometric shape functions and also first derivatives w.r.t. global coordinates at the ipt-th integration point. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const
	Compute the geometric shape functions (psi) and first derivatives w.r.t. global coordinates (dpsidx) at the ipt-th integration point. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of both "detJ" and "dpsidx" w.r.t. the nodal coordinates. More...

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d x^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Return the geometric shape functions and also first and second derivatives w.r.t. global coordinates at ipt-th integration point. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d s^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
	Overloaded version of the calculation of the local equation numbers. If the boolean argument is true then pointers to the degrees of freedom associated with each equation number are stored locally in the array Dof_pt. More...

Node *&	node_pt (const unsigned &n)
	Return a pointer to the local node n. More...

Node *const &	node_pt (const unsigned &n) const
	Return a pointer to the local node n (const version) More...

unsigned	nnode () const
	Return the number of nodes. More...

virtual unsigned	nnode_1d () const
	Return the number of nodes along one edge of the element Default is to return zero — must be overloaded by geometric elements. More...

double	raw_nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. Do not use the hanging node representation. NOTE: Moved to cc file because of a possible compiler bug in gcc (yes, really!). The move to the cc file avoids inlining which appears to cause problems (only) when compiled with gcc and -O3; offensive "illegal read" is in optimised-out section of code and data that is allegedly illegal is readily readable (by other means) just before this function is called so I can't really see how we could possibly be responsible for this... More...

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level). Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. If the node is hanging, the appropriate interpolation is handled by the position function in the Node class. More...

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level) Returns suitably interpolated version for hanging nodes. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. More...

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. More...

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. More...

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

unsigned	nnodal_position_type () const
	Return the number of coordinate types that the element requires to interpolate the geometry between the nodes. For Lagrange elements it is 1. More...

bool	has_hanging_nodes () const
	Return boolean to indicate if any of the element's nodes are geometrically hanging. More...

unsigned	nodal_dimension () const
	Return the required Eulerian dimension of the nodes in this element. More...

virtual Node *	construct_node (const unsigned &n)
	Construct the local node n and return a pointer to the newly created node object. More...

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n)
	Construct the local node n as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

int	get_node_number (Node *const &node_pt) const
	Return the number of the node *node_pt if this node is in the element, else return -1;. More...

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	If there is a node at this local coordinate, return the pointer to the node. More...

double	raw_nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n but do NOT take hanging nodes into account. More...

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps), but do NOT take hanging nodes into account. More...

double	nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n. Produces suitably interpolated values for hanging nodes. More...

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps). Produces suitably interpolated values for hanging nodes. More...

unsigned	dim () const
	Return the spatial dimension of the element, i.e. the number of local coordinates required to parametrise its geometry. More...

virtual double	interpolated_x (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s. More...

virtual double	interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s at previous timestep t (t=0: present; t>0: previous timestep) More...

virtual void	interpolated_x (const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s as Vector. More...

virtual void	interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s at previous timestep t as Vector (t=0: present; t>0: previous timestep) More...

virtual double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)
	Return t-th time-derivative of the i-th FE-interpolated Eulerian coordinate at local coordinate s. More...

virtual void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)
	Compte t-th time-derivative of the FE-interpolated Eulerian coordinate vector at local coordinate s. More...

unsigned	ngeom_data () const
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

Data *	geom_data_pt (const unsigned &j)
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

void	position (const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its incarnation as a GeomObject, r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s). More...

void	position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its GeomObject incarnation: r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s) This version of the function returns the position as a function of time t=0: current time; t>0: previous timestep. Works for t=0 but needs to be overloaded if genuine time-dependence is required. More...

void	dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)
	Return the t-th time derivative of the parametrised position of the FiniteElement in its GeomObject incarnation: $\frac{d^{t} dr(zeta)}{d t^{t}}$ . Call the t-th time derivative of the FE-interpolated Eulerian coordinate. More...

virtual double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
	Specify the values of the "global" intrinsic coordinate, zeta, of a compound geometric object (a mesh of elements) when the element is viewied as a sub-geometric object. The default assumption is that the element will be treated as a sub-geometric object in a bulk Mesh of other elements (geometric objects). The "global" coordinate of the compound geometric object is simply the Eulerian coordinate, x. The second default assumption is that the coordinate zeta will be stored at the nodes and interpolated using the shape functions of the element. This function returns the value of zeta stored at local node n, where k is the type of coordinate and i is the coordinate direction. The function is virtual so that it can be overloaded by different types of element: FaceElements and SolidFiniteElements. More...

void	interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const
	Calculate the interpolated value of zeta, the intrinsic coordinate of the element when viewed as a compound geometric object within a Mesh as a function of the local coordinate of the element, s. The default assumption is the zeta is interpolated using the shape functions of the element with the values given by zeta_nodal(). A MacroElement representation of the intrinsic coordinate parametrised by the local coordinate s is used if available. Choosing the MacroElement representation of zeta (Eulerian x by default) allows a correspondence to be established between elements on different Meshes covering the same curvilinear domain in cases where one element is much coarser than the other. More...

void	locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)
	For a given value of zeta, the "global" intrinsic coordinate of a mesh of FiniteElements represented as a compound geometric object, find the local coordinate in this element that corresponds to the requested value of zeta. If zeta cannot be located in this element, geom_object_pt is set to NULL. If zeta is located in this element, we return its "this" pointer. By default don't use any value passed in to the local coordinate s as the initial guess in the Newton method. More...

virtual void	node_update ()
	Update the positions of all nodes in the element using each node update function. The default implementation may be overloaded so that more efficient versions can be written. More...

virtual void	identify_geometric_data (std::set< Data * > &geometric_data_pt)
	The purpose of this function is to identify all `Data` objects that affect the elements' geometry. This function is implemented as an empty virtual function since it can only be implemented in conjunction with a node-update strategy. A specific implementation is provided in the ElementWithMovingNodes class. More...

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const
	Calculate the size of the element (length, area, volume,...) in Eulerian computational coordinates. Use suitably overloaded compute_physical_size() function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

virtual double	compute_physical_size () const
	Broken virtual function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

virtual void	point_output_data (const Vector< double > &s, Vector< double > &data)
	Virtual function to write the double precision numbers that appear in a single line of output into the data vector. Empty virtual, can be overloaded for specific elements; used e.g. by LineVisualiser. More...

void	point_output (std::ostream &outfile, const Vector< double > &s)
	Output solution (as defined by point_output_data()) at local cordinates s. More...

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const
	Return the number of actual plot points for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const
	Return the number of local sub-elements for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const
	Paraview output – this outputs the coordinates at the plot points (for parameter nplot) to specified output file. More...

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const
	Fill in the offset information for paraview plot. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const
	Return the paraview element type. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const
	Return the offsets for the paraview sub-elements. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual unsigned	nscalar_paraview () const
	Number of scalars/fields output by this element. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual std::string	scalar_name_paraview (const unsigned &i) const
	Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements. More...

virtual void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const
	Output the element data at time step t. This is const because it is newly added and so can be done easily. Really all the output(...) functions should be const! More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output a time-dependent exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
	Output a time-dependent exact solution over the element. More...

virtual void	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const
	Get cector of local coordinates of plot point i (when plotting nplot points in each "coordinate direction"). Generally these plot points will be uniformly spaced across the element. The optional final boolean flag (default: false) allows them to be shifted inwards to avoid duplication of plot point points between elements – useful when they are used in locate_zeta, say. More...

virtual std::string	tecplot_zone_string (const unsigned &nplot) const
	Return string for tecplot zone header (when plotting nplot points in each "coordinate direction") More...

virtual void	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const
	Add tecplot zone "footer" to output stream (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual void	write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const
	Add tecplot zone "footer" to C-style output. (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual unsigned	nplot_points (const unsigned &nplot) const
	Return total number of plot points (when plotting nplot points in each "coordinate direction") More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the norm of the error and that of the exact solution. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Plot the error when compared against a given time-dependent exact solution ${\bf f}(t,{\bf x})$ . Also calculates the norm of the error and that of the exact solution. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Plot the error when compared against a given time-dependent exact solution ${\bf f}(t,{\bf x})$ . Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the maximum absolute error. More...

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Evaluate integral of a Vector-valued function ${\bf f}({\bf x})$ over the element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Evaluate integral of a Vector-valued, time-dependent function ${\bf f}(t,{\bf x})$ over the element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)
	Function for building a lower dimensional FaceElement on the specified face of the FiniteElement. The arguments are the index of the face, an integer whose value depends on the particular element type, and a pointer to the FaceElement. More...

virtual unsigned	self_test ()
	Self-test: Check inversion of element & do self-test for GeneralisedElement. Return 0 if OK. More...

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const
	Get the number of the ith node on face face_index (in the bulk node vector). More...

virtual int	face_outer_unit_normal_sign (const int &face_index) const
	Get the sign of the outer unit normal on the face given by face_index. More...

void	face_node_number_error_check (const unsigned &i) const
	Range check for face node numbers. More...

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const
	Get a pointer to the function mapping face coordinates to bulk coordinates. More...

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const
	Get a pointer to the derivative of the mapping from face to bulk coordinates. More...

Public Member Functions inherited from oomph::GeneralisedElement
GeneralisedElement()	GeneralisedElement (const GeneralisedElement &)=delete
	Constructor: Initialise all pointers and all values to zero. More...

void	operator= (const GeneralisedElement &)=delete
	Broken assignment operator. More...

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const
	Return the global equation number corresponding to the ieqn_local-th local equation number. More...

int	local_eqn_number (const unsigned long &ieqn_global) const
	Return the local equation number corresponding to the ieqn_global-th global equation number. Returns minus one (-1) if there is no local degree of freedom corresponding to the chosen global equation number. More...

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) external data object to the element and return its index (i.e. the index required to obtain it from the access function `external_data_pt(...)`. The optional boolean flag indicates whether the data should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite-differencing. More...

bool	external_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the external data is included in the finite difference loop. More...

void	exclude_external_data_fd (const unsigned &i)
	Set the boolean flag to exclude the external datum from the the finite difference loop when computing the jacobian matrix. More...

void	include_external_data_fd (const unsigned &i)
	Set the boolean flag to include the external datum in the the finite difference loop when computing the jacobian matrix. More...

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
	Set the timestepper associated with the i-th internal data object. More...

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)
	Assign the global equation numbers to the internal Data. The arguments are the current highest global equation number (which will be incremented) and a Vector of pointers to the global variables (to which any unpinned values in the internal Data are added). More...

void	describe_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)
	Add pointers to the internal data values to map indexed by the global equation number. More...

void	add_internal_data_values_to_vector (Vector< double > &vector_of_values)
	Add all internal data and time history values to the vector in the internal storage order. More...

void	read_internal_data_values_from_vector (const Vector< double > &vector_of_values, unsigned &index)
	Read all internal data and time history values from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

void	add_internal_eqn_numbers_to_vector (Vector< long > &vector_of_eqn_numbers)
	Add all equation numbers associated with internal data to the vector in the internal storage order. More...

void	read_internal_eqn_numbers_from_vector (const Vector< long > &vector_of_eqn_numbers, unsigned &index)
	Read all equation numbers associated with internal data from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)
	Setup the arrays of local equation numbers for the element. If the optional boolean argument is true, then pointers to the associated degrees of freedom are stored locally in the array Dof_pt. More...

virtual void	complete_setup_of_dependencies ()
	Complete the setup of any additional dependencies that the element may have. Empty virtual function that may be overloaded for specific derived elements. Used, e.g., for elements with algebraic node update functions to determine the "geometric Data", i.e. the Data that affects the element's shape. This function is called (for all elements) at the very beginning of the equation numbering procedure to ensure that all dependencies are accounted for. More...

virtual void	get_residuals (Vector< double > &residuals)
	Calculate the vector of residuals of the equations in the element. By default initialise the vector to zero and then call the fill_in_contribution_to_residuals() function. Note that this entire function can be overloaded if desired. More...

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the elemental Jacobian matrix "d equation / d variable". More...

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and the elemental "mass" matrix, the matrix that multiplies the time derivative terms in a problem. More...

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and jacobian and elemental "mass" matrix, the matrix that multiplies the time derivative terms. More...

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Calculate the derivatives of the residuals with respect to a parameter. More...

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Calculate the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. More...

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
	Calculate the derivatives of the elemental Jacobian matrix mass matrix and residuals with respect to a parameter. More...

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Calculate the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Return the vector of inner product of the given pairs of history values. More...

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Compute the vectors that when taken as a dot product with other history values give the inner product over the element. More...

virtual void	compute_norm (Vector< double > &norm)
	Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific element. More...

virtual void	compute_norm (double &norm)
	Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific element. More...

void	set_halo (const unsigned &non_halo_proc_ID)
	Label the element as halo and specify processor that holds non-halo counterpart. More...

void	set_nonhalo ()
	Label the element as not being a halo. More...

bool	is_halo () const
	Is this element a halo? More...

int	non_halo_proc_ID ()
	ID of processor ID that holds non-halo counterpart of halo element; negative if not a halo. More...

void	set_must_be_kept_as_halo ()
	Insist that this element be kept as a halo element during a distribute? More...

void	unset_must_be_kept_as_halo ()
	Do not insist that this element be kept as a halo element during distribution. More...

bool	must_be_kept_as_halo () const
	Test whether the element must be kept as a halo element. More...

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const
	Create a list of pairs for the unknowns that this element is "in charge of" – ignore any unknowns associated with external `Data`. The first entry in each pair must contain the global equation number of the unknown, while the second one contains the number of the DOF type that this unknown is associated with. (The function can obviously only be called if the equation numbering scheme has been set up.) More...

Public Member Functions inherited from oomph::GeomObject
	GeomObject ()
	Default constructor. More...

	GeomObject (const unsigned &ndim)
	Constructor: Pass dimension of geometric object (# of Eulerian coords = # of Lagrangian coords; no time history available/needed) More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)
	Constructor: pass # of Eulerian and Lagrangian coordinates. No time history available/needed. More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)
	Constructor: pass # of Eulerian and Lagrangian coordinates and pointer to time-stepper which is used to handle the position at previous timesteps and allows the evaluation of veloc/acceleration etc. in cases where the GeomData varies with time. More...

	GeomObject (const GeomObject &dummy)=delete
	Broken copy constructor. More...

void	operator= (const GeomObject &)=delete
	Broken assignment operator. More...

virtual	~GeomObject ()
	(Empty) destructor More...

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()
	Access function for pointer to time stepper: Null if object is not time-dependent. More...

TimeStepper *	time_stepper_pt () const
	Access function for pointer to time stepper: Null if object is not time-dependent. Const version. More...

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const
	Parametrised position on object: r(zeta). Evaluated at the continuous time value, t. More...

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const
	Derivative of position Vector w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const
	2nd derivative of position Vector w.r.t. to coordinates: $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const
	Posn Vector and its 1st & 2nd derivatives w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

Public Member Functions inherited from oomph::RefineableLinearisedAxisymmetricNavierStokesEquations
	RefineableLinearisedAxisymmetricNavierStokesEquations ()
	Empty Constructor. More...

unsigned	num_Z2_flux_terms ()
	Number of 'flux' terms for Z2 error estimation. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Get 'flux' for Z2 error recovery: Upper triangular entries in strain rate tensor. More...

double	geometric_jacobian (const Vector< double > &x)
	Fill in the geometric Jacobian, which in this case is r. More...

Public Member Functions inherited from oomph::RefineableElement
	RefineableElement ()
	Constructor, calls the FiniteElement constructor and initialises the member data. More...

virtual	~RefineableElement ()
	Destructor, delete the allocated storage for the hanging equations. More...

	RefineableElement (const RefineableElement &)=delete
	Broken copy constructor. More...

void	operator= (const RefineableElement &)=delete
	Broken assignment operator. More...

Tree *	tree_pt ()
	Access function: Pointer to quadtree representation of this element. More...

void	set_tree_pt (Tree *my_tree_pt)
	Set pointer to quadtree representation of this element. More...

bool	refinement_is_enabled ()
	Flag to indicate suppression of any refinement. More...

void	disable_refinement ()
	Suppress of any refinement for this element. More...

void	enable_refinement ()
	Emnable refinement for this element. More...

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const
	Split the element into the number of sons to be constructed and return a vector of pointers to the sons. Elements are allocated, but they are not given any properties. The refinement level of the sons is one higher than that of the father elemern. More...

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)
	Access function that returns the local equation number for the hanging node variables (values stored at master nodes). The local equation number corresponds to the i-th unknown stored at the node addressed by node_pt. More...

void	set_refinement_level (const int &refine_level)
	Set the refinement level. More...

unsigned	refinement_level () const
	Return the Refinement level. More...

void	select_for_refinement ()
	Select the element for refinement. More...

void	deselect_for_refinement ()
	Deselect the element for refinement. More...

void	select_sons_for_unrefinement ()
	Unrefinement will be performed by merging the four sons of this element. More...

void	deselect_sons_for_unrefinement ()
	No unrefinement will be performed by merging the four sons of this element. More...

bool	to_be_refined ()
	Has the element been selected for refinement? More...

bool	sons_to_be_unrefined ()
	Has the element been selected for unrefinement? More...

virtual void	unbuild ()
	Unbuild the element, i.e. mark the nodes that were created during its creation for possible deletion. More...

virtual void	deactivate_element ()
	Final operations that must be performed when the element is no longer active in the mesh, but still resident in the QuadTree. More...

virtual bool	nodes_built ()
	Return true if all the nodes have been built, false if not. More...

long	number () const
	Element number (for debugging/plotting) More...

void	set_number (const long &mynumber)
	Set element number (for debugging/plotting) More...

virtual Node *	interpolating_node_pt (const unsigned &n, const int &value_id)
	In mixed elements, different sets of nodes are used to interpolate different unknowns. This function returns the n-th node that interpolates the value_id-th unknown. Default implementation is that all variables use the positional nodes, i.e. isoparametric elements. Note that any overloaded versions of this function MUST provide a set of nodes for the position, which always has the value_id -1. More...

virtual double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &value_id)
	Return the local one dimensional fraction of the n1d-th node in the direction of the local coordinate s[i] that is used to interpolate the value_id-th continuously interpolated unknown. Default assumes isoparametric interpolation for all unknowns. More...

virtual Node *	get_interpolating_node_at_local_coordinate (const Vector< double > &s, const int &value_id)
	Return a pointer to the node that interpolates the value-id-th unknown at local coordinate s. If there is not a node at that position, then return 0. More...

virtual unsigned	ninterpolating_node (const int &value_id)
	Return the number of nodes that are used to interpolate the value_id-th unknown. Default is to assume isoparametric elements. More...

virtual unsigned	ninterpolating_node_1d (const int &value_id)
	Return the number of nodes in a one_d direction that are used to interpolate the value_id-th unknown. Default is to assume an isoparametric mapping. More...

virtual void	interpolating_basis (const Vector< double > &s, Shape &psi, const int &value_id) const
	Return the basis functions that are used to interpolate the value_id-th unknown. By default assume isoparameteric interpolation. More...

void	identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)
	The purpose of this function is to identify all possible Data that can affect the fields interpolated by the FiniteElement. This must be overloaded to include data from any hanging nodes correctly. More...

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)
	Overload the function that assigns local equation numbers for the Data stored at the nodes so that hanging data is taken into account. More...

virtual RefineableElement *	root_element_pt ()
	Pointer to the root element in refinement hierarchy (must be implemented in specific elements that do refinement via tree-like refinement structure. Here we provide a default implementation that is appropriate for cases where tree-like refinement doesn't exist or if the element doesn't have root in that tree (i.e. if it's a root itself): We return "this". More...

virtual RefineableElement *	father_element_pt () const
	Return a pointer to the father element. More...

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)
	Return a pointer to the "father" element at the specified refinement level. More...

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)
	Initial setup of the element: e.g. set the appropriate internal p-order. If an adopted father is specified, information from this is used instead of using the father found from the tree. More...

virtual void	pre_build (Mesh &mesh_pt, Vector< Node > &new_node_pt)
	Pre-build the element. More...

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)
	Compute derivatives of elemental residual vector with respect to nodal coordinates. Default implementation by FD can be overwritten for specific elements. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij} This version is overloaded from the version in FiniteElement and takes hanging nodes into account – j in the above loop loops over all the nodes that actively control the shape of the element (i.e. they are non-hanging or master nodes of hanging nodes in this element). More...

unsigned	nshape_controlling_nodes ()
	Number of shape-controlling nodes = the number of non-hanging nodes plus the number of master nodes associated with hanging nodes. More...

std::map< Node *, unsigned >	shape_controlling_node_lookup ()
	Return lookup scheme for unique number associated with any of the nodes that actively control the shape of the element (i.e. they are either non-hanging nodes of this element or master nodes of hanging nodes. More...

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()
	A stuitable error estimator for a multi-physics elements may require one Z2 error estimate for each field (e.g. velocity and temperature in a fluid convection problem). It is assumed that these error estimates will each use selected flux terms. The number of compound fluxes returns the number of such combinations of the flux terms. Default value is one and all flux terms are combined with equal weight. More...

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)
	Plot the error when compared against a given exact flux. Also calculates the norm of the error and that of the exact flux. More...

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)
	Return the compound flux index of each flux component The default (do nothing behaviour) will mean that all indices remain at the default value zero. More...

Public Member Functions inherited from oomph::RefineableQElement< 2 >
	RefineableQElement ()
	Constructor: Pass refinement level (default 0 = root) More...

	RefineableQElement (const RefineableQElement< 2 > &dummy)=delete
	Broken copy constructor. More...

virtual	~RefineableQElement ()
	Broken assignment operator. More...

unsigned	required_nsons () const
	A refineable quad element has four sons. More...

virtual Node *	node_created_by_neighbour (const Vector< double > &s_fraction, bool &is_periodic)
	If a neighbouring element has already created a node at a position corresponding to the local fractional position within the present element, s_fraction, return a pointer to that node. If not, return NULL (0). If the node is on a periodic boundary the flag is_periodic is true, otherwise it will be false. More...

virtual Node *	node_created_by_son_of_neighbour (const Vector< double > &s_fraction, bool &is_periodic)
	If a son of a neighbouring element has already created a node at a position corresponding to the local fractional position within the present element, s_fraction, return a pointer to that node. If not, return NULL (0). If the node is on a periodic boundary the flag is_periodic is true, otherwise it will be false. More...

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)
	Build the element, i.e. give it nodal positions, apply BCs, etc. Pointers to any new nodes will be returned in new_node_pt. If it is open, the positions of the new nodes will be written to the file stream new_nodes_file. More...

void	check_integrity (double &max_error)
	Check the integrity of the element: ensure that the position and values are continuous across the element edges. More...

void	output_corners (std::ostream &outfile, const std::string &colour) const
	Print corner nodes, use colour. More...

QuadTree *	quadtree_pt ()
	Pointer to quadtree representation of this element. More...

QuadTree *	quadtree_pt () const
	Pointer to quadtree representation of this element. More...

void	setup_hanging_nodes (Vector< std::ofstream * > &output_stream)
	Markup all hanging nodes & document the results in the output streams contained in the vector output_stream, if they are open. More...

void	get_boundaries (const int &edge, std::set< unsigned > &boundaries) const
	Determine set of (mesh) boundaries that the element edge/vertex lives on. More...

void	get_bcs (int bound, Vector< int > &bound_cons) const
	Determine Vector of boundary conditions along edge (or on vertex) bound (S/W/N/E/SW/SE/NW/NE): For value ival on this boundary, bound_cons[ival]=1 if pinned and 0 if free. More...

void	interpolated_zeta_on_edge (const unsigned &boundary, const int &edge, const Vector< double > &s, Vector< double > &zeta)
	Return the value of the intrinsic boundary coordinate interpolated along the edge (S/W/N/E) More...

Public Member Functions inherited from oomph::QuadElementBase
	QuadElementBase ()
	Constructor. Empty. More...

Public Member Functions inherited from oomph::QElementBase
	QElementBase ()
	Constructor: Initialise pointers to macro element reference coords. More...

	QElementBase (const QElementBase &)=delete
	Broken copy constructor. More...

virtual	~QElementBase ()
	Broken assignment operator. More...

bool	local_coord_is_valid (const Vector< double > &s)
	Check whether the local coordinate are valid or not. More...

void	move_local_coord_back_into_element (Vector< double > &s) const
	Adjust local coordinates so that they're located inside the element. More...

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)
	Set pointer to macro element also sets up storage for the reference coordinates and initialises them. More...

double &	s_macro_ll (const unsigned &i)
	Access fct to the i-th coordinate of the element's "lower left" vertex in the associated MacroElement. More...

double &	s_macro_ur (const unsigned &i)
	Access fct to the i-th coordinate of the element's "upper right" vertex in the associated MacroElement. More...

double	s_macro_ll (const unsigned &i) const
	Access fct to the i-th coordinate of the element's "lower left" vertex in the associated MacroElement. (const version) More...

double	s_macro_ur (const unsigned &i) const
	Access fct to the i-th coordinate of the element's "upper right" vertex in the associated MacroElement. (const version) More...

void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates. using the macro element representation. More...

void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous) using the macro element representation. More...

unsigned	nnode_on_face () const
	Return number of nodes on one face of the element. Always nnode_1d^(el_dim - 1). More...

ElementGeometry::ElementGeometry	element_geometry () const
	It's a Q element! More...

Public Member Functions inherited from oomph::QElementGeometricBase
	QElementGeometricBase ()
	Empty default constructor. More...

	QElementGeometricBase (const QElementGeometricBase &)=delete
	Broken copy constructor. More...

Public Member Functions inherited from oomph::ElementWithExternalElement
	ElementWithExternalElement ()
	Constructor. Initialise member data and pointers to data associated with the external elements to zero. More...

virtual	~ElementWithExternalElement ()
	The destructor, clean up any allocated memory. More...

	ElementWithExternalElement (const ElementWithExternalElement &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithExternalElement &)=delete
	Broken assignment operator. More...

bool	storage_has_been_allocated () const
	Helper function to check if storage has actually been allocated. More...

FiniteElement *&	external_element_pt (const unsigned &interaction_index, const unsigned &ipt)
	Access function to source element for specified interaction index at specified integration point. More...

FiniteElement *const &	external_element_pt (const unsigned &interaction_index, const unsigned &ipt) const
	Access function to source element, const version. More...

Vector< double > &	external_element_local_coord (const unsigned &interaction_index, const unsigned &ipt)
	Access function to get source element's local coords for specified interaction index at specified integration point. More...

Vector< double > const &	external_element_local_coord (const unsigned &interaction_index, const unsigned &ipt) const
	Access function to get source element's coords, const version. More...

void	output_external_elements (std::ostream &outfile, const unsigned &interaction_index)
	Output by plotting vector from integration point to corresponding point in external element for specified interaction index. More...

void	initialise_external_element_storage ()
	Initialise storage for pointers to external elements and their local coordinates. This must be called before any of the access functions are used. More...

void	flush_all_external_element_storage ()
	Flush the storage for external elements. More...

void	set_ninteraction (const unsigned &n_interaction)
	Set the number of interactions in the element This function is usually called in the specific element's constructor. More...

unsigned	ninteraction () const
	Return the number of interactions in the element. More...

virtual void	identify_all_field_data_for_external_interaction (Vector< std::set< FiniteElement * >> const &external_elements_pt, std::set< std::pair< Data *, unsigned >> &paired_interaction_data)
	Function that must return all the data involved in the desired interactions from the external element. More...

virtual void	identify_all_geometric_data_for_external_interaction (Vector< std::set< FiniteElement * >> const &external_elements_pt, std::set< Data * > &external_geometric_data_pt)
	Function that must return all geometric data involved in the desired interactions from the external element. More...

unsigned	nexternal_interaction_field_data () const
	Return the number of Data items that affect the external interactions in this element. This includes e.g. fluid velocities and pressures in adjacent fluid elements in an FSI problem. More...

Vector< Data * >	external_interaction_field_data_pt () const
	Return vector of pointers to the field Data objects that affect the interactions on the element. More...

unsigned	nexternal_interaction_geometric_data () const
	Return the number of geometric Data items that affect the external interactions in this element: i.e. any geometric Data in the problem that affects the nodal positions in the external elements. More...

bool	add_external_geometric_data ()
	Are we including external geometric data in the element's Jacobian. More...

bool	add_external_interaction_data ()
	Are we including external data in the element's Jacobian. More...

Vector< Data * >	external_interaction_geometric_data_pt () const
	Return vector of pointers to the geometric Data objects that affect the interactions on the element. More...

void	ignore_external_geometric_data ()
	Do not include any external geometric data when computing the element's Jacobian. This function should be called if the external element does not move and/or if the "source term" does not depend on spatial derivatives of the field computed by the other element. More...

void	ignore_external_interaction_data ()
	Do not include any external interaction data when computing the element's Jacobian. More...

void	include_external_geometric_data ()
	Do include external geometric data when computing the element's Jacobian. This function should be called to re-enable inclusion of external geometric data. More...

void	include_external_interaction_data ()
	Do include external geometric data when computing the element's Jacobian This function should be called to re-enable inclusion of external interaction data. More...

bool	external_geometric_data_is_included () const
	Is the external geometric data taken into account when forming the Jacobian? More...

void	describe_local_dofs (std::ostream &out, const std::string &curr_string) const
	Function to describe the local dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

Additional Inherited Members
Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)
	Function pointer for function that computes vector-valued steady "exact solution" ${\bf f}({\bf x})$ as $\mbox{\tt fct}({\bf x}, {\bf f})$ . More...

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)
	Function pointer for function that computes Vector-valued time-dependent function ${\bf f}(t,{\bf x})$ as $\mbox{\tt fct}(t, {\bf x}, {\bf f})$ . More...

Public Types inherited from oomph::RefineableQElement< 2 >
typedef void(RefineableQElement< 2 >::*	VoidMemberFctPt) ()
	Shorthand for pointer to an argument-free void member function of the refineable element. More...

Static Public Member Functions inherited from oomph::RefineableLinearisedAxisymmetricNavierStokesEquations
static void	pin_redundant_nodal_pressures (const Vector< GeneralisedElement * > &element_pt)
	Loop over all elements in Vector (which typically contains all the elements in a fluid mesh) and pin the nodal pressure degrees of freedom that are not being used. Function uses the member function. More...

static void	unpin_all_pressure_dofs (const Vector< GeneralisedElement * > &element_pt)
	Unpin all pressure dofs in elements listed in Vector. More...

Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. More...

Public Attributes inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
void(*&)(const double &time, const Vector< double > &x, Vector< double > &f)	base_flow_u_fct_pt ()
	Access function for the base flow solution pointer. More...

void(*&)(const double &time, const Vector< double > &x, DenseMatrix< double > &f)	base_flow_dudx_fct_pt ()
	Access function for the derivatives of the base flow w.r.t. global coordinates solution pointer. More...

Static Public Attributes inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
static Vector< double >	Gamma
	Vector to decide whether the stress-divergence form is used or not. More...

Static Public Attributes inherited from oomph::FiniteElement
static double	Tolerance_for_singular_jacobian = 1.0e-16
	Tolerance below which the jacobian is considered singular. More...

static bool	Accept_negative_jacobian = false
	Boolean that if set to true allows a negative jacobian in the transform between global and local coordinates (negative surface area = left-handed coordinate system). More...

static bool	Suppress_output_while_checking_for_inverted_elements
	Static boolean to suppress output while checking for inverted elements. More...

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data
	Static boolean to suppress warnings about repeated internal data. Defaults to false. More...

static bool	Suppress_warning_about_repeated_external_data = true
	Static boolean to suppress warnings about repeated external data. Defaults to true. More...

static double	Default_fd_jacobian_step = 1.0e-8
	Double used for the default finite difference step in elemental jacobian calculations. More...

Protected Member Functions inherited from oomph::LinearisedAxisymmetricQCrouzeixRaviartElement
double	dshape_and_dtest_eulerian_linearised_axi_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
	Velocity shape and test functions and their derivatives w.r.t. global coordinates at local coordinate s (taken from geometry). Return Jacobian of mapping between local and global coordinates. More...

double	dshape_and_dtest_eulerian_at_knot_linearised_axi_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
	Velocity shape and test functions and their derivatives w.r.t. global coordinates at the ipt-th integation point (taken from geometry). Return Jacobian of mapping between local and global coordinates. More...

void	pshape_linearised_axi_nst (const Vector< double > &s, Shape &psi) const
	Compute the pressure shape functions at local coordinate s. More...

void	pshape_linearised_axi_nst (const Vector< double > &s, Shape &psi, Shape &test) const
	Compute the pressure shape and test functions at local coordinate s. More...

Protected Member Functions inherited from oomph::FiniteElement
template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Take the matrix passed as jacobian and return its inverse in inverse_jacobian. This function is templated by the dimension of the element because matrix inversion cannot be written efficiently in a generic manner. More...

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	A template-free interface that takes the matrix passed as jacobian and return its inverse in inverse_jacobian. By default the function will use the dimension of the element to call the correct invert_jacobian(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

virtual double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates. Returns the determinant of the jacobian, the jacobian and inverse jacobian. More...

double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates, Return only the determinant of the jacobian and the inverse of the mapping (ds/dx). More...

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	A template-free interface that calculates the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. To do this it requires the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. By default the function will use the dimension of the element to call the correct dJ_eulerian_dnodal_coordinates_templated_helper(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij using the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. This function is templated by the dimension of the element. More...

virtual void	d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	A template-free interface that calculates the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions $\psi_j$ w.r.t. the global eulerian coordinates . I.e. this function calculates. More...

template<unsigned DIM>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates , using the determinant of the jacobian mapping, its derivative w.r.t. the nodal coordinates $X_{pq}$ , the inverse jacobian and the derivatives of the shape functions w.r.t. the local coordinates. The result is returned as a tensor of rank four. Numbering: d_dpsidx_dX(p,q,j,i) = $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right)$ This function is templated by the dimension of the element. More...

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t.local coordinates to derivatives w.r.t the coordinates used to assemble the inverse_jacobian passed in the mapping. On entry, dbasis must contain the basis function derivatives w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates on exit. This is virtual so that it may be overloaded if desired for efficiency reasons. More...

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian passed in the mapping, assuming that the coordinates are aligned in the direction of the local coordinates. On entry dbasis must contain the derivatives of the basis functions w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates. are converted into the new using the mapping inverse_jacobian. More...

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordiantes to derivatives and second derivatives w.r.t. the coordinates used to assemble the jacobian, inverse jacobian and jacobian2 passed to the function. By default this function will call transform_second_derivatives_template<>(...) using the dimension of the element as the template parameter. It is virtual so that it can be overloaded by a specific element to save using a switch statement. Optionally, the element writer may wish to use the transform_second_derivatives_diagonal<>(...) function On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

template<unsigned DIM>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This is templated by dimension because the method of calculation varies significantly with the dimension. On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

template<unsigned DIM>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This version of the function assumes that the local coordinates are aligned with the global coordinates, i.e. the jacobians are diagonal On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

virtual void	update_before_nodal_fd ()
	Function that is called before the finite differencing of any nodal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_nodal_fd ()
	Function that is call after the finite differencing of the nodal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after a change in the i-th nodal value. More...

virtual void	reset_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after the i-th nodal values is reset. The default behaviour is to call the update function. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Zero-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	One-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Two-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Three-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Zero-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	One-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Two-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Three-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Zero-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	One-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Two-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Three-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly. Specialisation to two spatial dimensions. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert second derivatives w.r.t. local coordinates to second derivatives w.r.t. the coordinates passed in the tensor coordinate. Specialised to two spatial dimension. More...

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) internal data object to the element and return the index required to obtain it from the access function `internal_data_pt()`. The boolean indicates whether the datum should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite differencing. More...

bool	internal_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the internal data is included in the finite difference loop. More...

void	exclude_internal_data_fd (const unsigned &i)
	Set the boolean flag to exclude the internal datum from the finite difference loop when computing the jacobian matrix. More...

void	include_internal_data_fd (const unsigned &i)
	Set the boolean flag to include the internal datum in the finite difference loop when computing the jacobian matrix. More...

void	clear_global_eqn_numbers ()
	Clear the storage for the global equation numbers and pointers to dofs (if stored) More...

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)
	Add the contents of the queue global_eqn_numbers to the local storage for the local-to-global translation scheme. It is essential that the entries in the queue are added IN ORDER i.e. from the front. More...

virtual void	assign_additional_local_eqn_numbers ()
	Setup any additional look-up schemes for local equation numbers. Examples of use include using local storage to refer to explicit degrees of freedom. The additional memory cost of such storage may or may not be offset by fast local access. More...

int	internal_local_eqn (const unsigned &i, const unsigned &j) const
	Return the local equation number corresponding to the j-th value stored at the i-th internal data. More...

int	external_local_eqn (const unsigned &i, const unsigned &j)
	Return the local equation number corresponding to the j-th value stored at the i-th external data. More...

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all external data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

virtual void	update_before_internal_fd ()
	Function that is called before the finite differencing of any internal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_internal_fd ()
	Function that is call after the finite differencing of the internal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after a change in any values in the i-th internal data object. More...

virtual void	reset_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	update_before_external_fd ()
	Function that is called before the finite differencing of any external data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_external_fd ()
	Function that is call after the finite differencing of the external data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after a change in any values in the i-th external data object. More...

virtual void	reset_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Add the elemental contribution to the mass matrix matrix. and the residuals vector. Note that this function should NOT initialise the residuals vector or the mass matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is deliberately broken. More...

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Add the elemental contribution to the derivatives of the residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More...

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Add the elemental contribution to the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More...

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
	Add the elemental contribution to the derivative of the jacobian matrix, mass matrix and the residuals vector with respect to the passed parameter. Note that this function should NOT initialise any entries. It must be called after the residuals vector and matrices have been initialised to zero. More...

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Fill in contribution to the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Fill in the contribution to the inner products between given pairs of history values. More...

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Fill in the contributions to the vectors that when taken as dot product with other history values give the inner product over the element. More...

Protected Member Functions inherited from oomph::RefineableLinearisedAxisymmetricNavierStokesEquations
virtual Node *	pressure_node_pt (const unsigned &n_p)
	Pointer to n_p-th pressure node (Default: NULL, indicating that pressure is not based on nodal interpolation). More...

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()
	Pin unused nodal pressure dofs (empty by default, because by default pressure dofs are not associated with nodes) More...

Protected Member Functions inherited from oomph::RefineableElement
void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const
	Assemble the jacobian matrix for the mapping from local to Eulerian coordinates, given the derivatives of the shape function w.r.t the local coordinates. Overload the standard version to use the hanging information for the Eulerian coordinates. More...

void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const
	Assemble the the "jacobian" matrix of second derivatives of the mapping from local to Eulerian coordinates, given the second derivatives of the shape functions w.r.t. local coordinates. Overload the standard version to use the hanging information for the Eulerian coordinates. More...

void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const
	Assemble the covariant Eulerian base vectors, assuming that the derivatives of the shape functions with respect to the local coordinates have already been constructed. Overload the standard version to account for hanging nodes. More...

double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates given the derivatives of the shape functions w.r.t the local coordinates. assuming that the coordinates are aligned in the direction of the local coordinates, i.e. there are no cross terms and the jacobian is diagonal. This funciton returns the determinant of the jacobian, the jacobian and the inverse jacobian. Overload the standard version to take hanging info into account. More...

void	assign_hanging_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for hanging node variables. More...

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version is overloaded to take hanging node information into account. More...

Protected Member Functions inherited from oomph::RefineableQElement< 2 >
void	setup_father_bounds ()
	Setup static matrix for coincidence between son nodal points and father boundaries. More...

void	get_edge_bcs (const int &edge, Vector< int > &bound_cons) const
	Determine Vector of boundary conditions along edge (N/S/W/E) More...

void	setup_hang_for_value (const int &value_id)
	Internal helper function that is used to construct the hanging node schemes for the value_id-th interpolated value. More...

virtual void	quad_hang_helper (const int &value_id, const int &my_edge, std::ofstream &output_hangfile)
	Internal helper function that is used to construct the hanging node schemes for the positions. More...

Protected Member Functions inherited from oomph::ElementWithExternalElement
void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)
	Overload the assign internal and external local equation number scheme so that the interaction data is taken into account. More...

void	assign_external_interaction_data_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for those Data values involved in the external interactions that affect the residuals of the element. More...

void	fill_in_jacobian_from_external_interaction_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from all external interaction degrees of freedom (geometric and field data) in the external element using finite differences. This version of the function assumes that the residuals vector has already been calculated. More...

void	fill_in_jacobian_from_external_interaction_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from all enternal interaction degrees of freedom (geometric and field data) in the external element using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

void	fill_in_jacobian_from_external_interaction_field_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the external interaction degrees of freedom associated with fields interpolated by the external element using finite differences. This version of the function assumes that the residuals vector has already been calculated. More...

void	fill_in_jacobian_from_external_interaction_field_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the enternal interaction degrees of freedom associated with fields interpolated by the external element using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

void	fill_in_jacobian_from_external_interaction_geometric_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the external interaction degrees of freedom associated with the geometry of the external elements using finite differences. This version of the function assumes that the residuals vector has already been calculated. More...

void	fill_in_jacobian_from_external_interaction_geometric_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the external interaction degrees of freedom associated with the geometry of the external elements using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

virtual void	update_before_external_interaction_field_fd ()
	Function that is called before the finite differencing of any external interaction data associated with external fields. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_external_interaction_field_fd ()
	Function that is call after the finite differencing of the external interaction data associated with external fields This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_external_interaction_field_fd (const unsigned &i)
	Function called within the finite difference loop for external interaction data after a change in any values in the i-th external interaction data object associated with external fields. More...

virtual void	reset_in_external_interaction_field_fd (const unsigned &i)
	Function called within the finite difference loop for external interaction data after the values in the i-th external interaction data object associated with external fields are reset. The default behaviour is to call the update function. More...

virtual void	update_before_external_interaction_geometric_fd ()
	Function that is called before the finite differencing of any external interaction data associated with external geometry. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_external_interaction_geometric_fd ()
	Function that is call after the finite differencing of the external interaction data associated with external geometry. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_external_interaction_geometric_fd (const unsigned &i)
	Function called within the finite difference loop for external interaction data after a change in any values in the i-th external interaction data object associated with external geometry. More...

virtual void	reset_in_external_interaction_geometric_fd (const unsigned &i)
	Function called within the finite difference loop for external interaction data after the values in the i-th external interaction data object associated with external geometry are reset. The default behaviour is to call the update function. More...

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)
	Static helper function that is used to check that the value_id is in range. More...

Protected Attributes inherited from oomph::LinearisedAxisymmetricQCrouzeixRaviartElement
Vector< unsigned >	P_linearised_axi_nst_internal_index
	Internal indices that indicate at which internal data the pressure values are stored. We note that there are two pressure values, corresponding to the functions P^C(r,z,t) and P^S(r,z,t) which multiply the cosine and sine terms respectively. More...

Protected Attributes inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
double *	Viscosity_Ratio_pt
	Pointer to the viscosity ratio (relative to the viscosity used in the definition of the Reynolds number) More...

double *	Density_Ratio_pt
	Pointer to the density ratio (relative to the density used in the definition of the Reynolds number) More...

double *	Re_pt
	Pointer to global Reynolds number. More...

double *	ReSt_pt
	Pointer to global Reynolds number x Strouhal number (=Womersley) More...

int *	Azimuthal_Mode_Number_pt
	Pointer to azimuthal mode number k in e^ik(theta) decomposition. More...

void(*	Base_flow_u_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to base flow solution (velocity components) function. More...

void(*	Base_flow_dudx_fct_pt )(const double &time, const Vector< double > &x, DenseMatrix< double > &result)
	Pointer to derivatives of base flow solution velocity components w.r.t. global coordinates (r and z) function. More...

bool	ALE_is_disabled
	Boolean flag to indicate if ALE formulation is disabled when the time-derivatives are computed. Only set to true if you're sure that the mesh is stationary. More...

Protected Attributes inherited from oomph::FiniteElement
MacroElement *	Macro_elem_pt
	Pointer to the element's macro element (NULL by default) More...

Protected Attributes inherited from oomph::GeneralisedElement
int	Non_halo_proc_ID
	Non-halo processor ID for Data; -1 if it's not a halo. More...

bool	Must_be_kept_as_halo
	Does this element need to be kept as a halo element during a distribute? More...

Protected Attributes inherited from oomph::GeomObject
unsigned	NLagrangian
	Number of Lagrangian (intrinsic) coordinates. More...

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt
	Timestepper (used to handle access to geometry at previous timesteps) More...

Protected Attributes inherited from oomph::RefineableElement
Tree *	Tree_pt
	A pointer to a general tree object. More...

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

bool	Refinement_is_enabled
	Flag to indicate suppression of any refinement. More...

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

long	Number
	Global element number – for plotting/validation purposes. More...

Protected Attributes inherited from oomph::ElementWithExternalElement
bool	Add_external_interaction_data
	Boolean flag to indicate whether to include the external data. More...

bool	Add_external_geometric_data
	Boolean flag to indicate whether to include the external geometric data. More...

Data **	External_interaction_field_data_pt
	/ Storage for pointers to external field Data that affect the interactions in the elemenet More...

Data **	External_interaction_geometric_data_pt
	/ Storage for pointers to external geometric Data that affect the interactions in the elemenet More...

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default return value for required_nvalue(n) which gives the number of "data" values required by the element at node n; for example, solving a Poisson equation would required only one "data" value at each node. The defaults is set to zero, because a general element is problem-less. More...

static const double	Node_location_tolerance = 1.0e-14
	Default value for the tolerance to be used when locating nodes via local coordinates. More...

static const unsigned	N2deriv [] = {0, 1, 3, 6}
	Static array that holds the number of second derivatives as a function of the dimension of the element. More...

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix
	Empty dense matrix used as a dummy argument to combined residual and jacobian functions in the case when only the residuals are being assembled. More...

static std::deque< double * >	Dof_pt_deque
	Static storage for deque used to add_global_equation_numbers when pointers to the dofs in each element are not required. More...

Static Protected Attributes inherited from oomph::RefineableElement
static double	Max_integrity_tolerance = 1.0e-8
	Max. allowed discrepancy in element integrity check. More...

Static Protected Attributes inherited from oomph::RefineableQElement< 2 >
static std::map< unsigned, DenseMatrix< int > >	Father_bound
	Coincidence between son nodal points and father boundaries: Father_bound[node_1d](jnod_son,son_type)={SW/SE/NW/NE/S/E/N/W/OMEGA}. More...

Detailed Description

////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////

Build a RefineableLinearisedAxisymmetricQCrouzeixRaviart element that inherits from ElementWithExternalElement so that it can "communicate" with an axisymmetric Navier-Stokes element that provides the base flow velocities and their derivatives w.r.t. global coordinates (r and z)

Definition at line 412 of file multi_domain_linearised_axisym_navier_stokes_elements.h.

Constructor & Destructor Documentation

◆ RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement()

RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement::RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement ( )

inline

Constructor: call the underlying constructors.

Do not include any external geometric data when computing the element's Jacobian.

Definition at line 418 of file multi_domain_linearised_axisym_navier_stokes_elements.h.

References oomph::ElementWithExternalElement::ignore_external_geometric_data(), and oomph::ElementWithExternalElement::ignore_external_interaction_data().

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

void RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Compute the element's residual vector and the Jacobian matrix.

Reimplemented from oomph::ElementWithExternalElement.

Definition at line 508 of file multi_domain_linearised_axisym_navier_stokes_elements.h.

References oomph::LinearisedAxisymmetricNavierStokesEquations::fill_in_contribution_to_jacobian().

◆ get_base_flow_dudx()

virtual void RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement::get_base_flow_dudx	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	x,
		DenseMatrix< double > &	result
	)		const

inlinevirtual

Overload get_base_flow_dudx(...) to return the derivatives of the external element's velocity components w.r.t. global coordinates at the integration point.

Reimplemented from oomph::LinearisedAxisymmetricNavierStokesEquations.

Definition at line 470 of file multi_domain_linearised_axisym_navier_stokes_elements.h.

References i, and oomph::AxisymmetricNavierStokesEquations::interpolated_dudx_axi_nst().

◆ get_base_flow_u()

virtual void RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement::get_base_flow_u	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	x,
		Vector< double > &	result
	)		const

inlinevirtual

Overload get_base_flow_u(...) to return the external element's velocity components at the integration point.

Reimplemented from oomph::LinearisedAxisymmetricNavierStokesEquations.

Definition at line 437 of file multi_domain_linearised_axisym_navier_stokes_elements.h.

References i, and oomph::AxisymmetricNavierStokesEquations::interpolated_u_axi_nst().

The documentation for this class was generated from the following file:

multi_domain_linearised_axisym_navier_stokes_elements.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableLinearisedAxisymmetricQCrouzeixRaviartMultiDomainElement()

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

◆ get_base_flow_dudx()

◆ get_base_flow_u()