Public Member Functions | List of all members
oomph::TBubbleEnrichedElementShape< 3, 3 > Class Reference

Standard quadratic shape functions enriched by the addition of three cubic "face" bubbles and quartic "volume" bubble, which consists of adding a node at the centroid of each face and a single node at the centroid of the tetrahedron. More...

#include <Telements.h>

Public Member Functions

unsigned n_enriched_nodes ()
 
void local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
 
void shape (const Vector< double > &s, Shape &psi) const
 Shape function for specific TBubbleEnrichedElement<3,3>
 
void dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
 Derivatives of shape functions for specific TElement<3,3>
 
void d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
 Second derivatives of shape functions for specific TElement<3,3>: 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 $.
 

Detailed Description

Standard quadratic shape functions enriched by the addition of three cubic "face" bubbles and quartic "volume" bubble, which consists of adding a node at the centroid of each face and a single node at the centroid of the tetrahedron.

Return local coordinates of node j

Definition at line 2312 of file Telements.h.

Member Function Documentation

◆ d2shape_local()

void oomph::TBubbleEnrichedElementShape< 3, 3 >::d2shape_local ( const Vector< double > &  s,
Shape &  psi,
DShape &  dpsids,
DShape &  d2psids 
) const
inline

Second derivatives of shape functions for specific TElement<3,3>: 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 $.

Definition at line 2689 of file Telements.h.

References s.

◆ dshape_local()

void oomph::TBubbleEnrichedElementShape< 3, 3 >::dshape_local ( const Vector< double > &  s,
Shape &  psi,
DShape &  dpsids 
) const
inline

Derivatives of shape functions for specific TElement<3,3>

Definition at line 2494 of file Telements.h.

References s.

◆ local_coordinate_of_node()

void oomph::TBubbleEnrichedElementShape< 3, 3 >::local_coordinate_of_node ( const unsigned &  j,
Vector< double > &  s 
) const
inline

Definition at line 2320 of file Telements.h.

References s.

◆ n_enriched_nodes()

unsigned oomph::TBubbleEnrichedElementShape< 3, 3 >::n_enriched_nodes ( )
inline

Definition at line 2315 of file Telements.h.

◆ shape()

void oomph::TBubbleEnrichedElementShape< 3, 3 >::shape ( const Vector< double > &  s,
Shape &  psi 
) const
inline

Shape function for specific TBubbleEnrichedElement<3,3>

Definition at line 2438 of file Telements.h.

References s.

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