Dune::P1CubeShapeFunction

Dune::P1CubeShapeFunction< C, T, d > Class Template Reference
[Shapefunctions]

#include <cubeshapefunctions.hh>

List of all members.

Detailed Description

template<typename C, typename T, int d>
class Dune::P1CubeShapeFunction< C, T, d >

A class for piecewise bilinear shape functions in the cube. This class implements the interface of ShapeFunction but is NOT derived from it to avoid making the functions virtual at this stage.

Let i=(i_{dim-1},...,i_1,i_0) be the binary representation of the shape function number. Then the corresponding shape function can be written as

phi_i (x) = {j=0}^{dim-1} [ 1-i_j + x_j*(2*i_j-1) ]

and its derivative is

d/dx_k phi_i (x) = (2*i_k-1) * {j!=k} [ 1-i_j + x_j*(2*i_j-1) ]

The coefficients a_{ij} = 1-i_j and b_{ij} = 2*i_j-1 are precomputed.


Public Member Functions

 P1CubeShapeFunction (int i)
 make a shape function object
 P1CubeShapeFunction ()
 must be defaultconstructible
ResultType evaluateFunction (int comp, const FieldVector< CoordType, d > &x) const
 evaluate shape function in local coordinates
ResultType evaluateDerivative (int comp, int dir, const FieldVector< CoordType, d > &x) const
 evaluate gradient in local coordinates
int localindex (int comp) const
 consecutive number of associated dof within element
int codim () const
 codim of associated dof
int entity () const
 entity (of codim) of associated dof
int entityindex () const
 consecutive number of dof within entity
const FieldVector< CoordType,
dim > & 		position () const
 interpolation point associated with shape function
The documentation for this class was generated from the following file:

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