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

#include <shapefunctions.hh>

Inheritance diagram for Dune::ShapeFunction< C, T, d, N >:

List of all members.

Detailed Description

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

Abstract base class for a shape function.

A shape function $\phi : \Omega_E \to R^N$ has the following properties:

It is a function defined on the reference element $\Omega_E \subset R^d$ .
It is associated with a degree of freedom of the finite element space.
A transformation from the reference element to the actual element yields a finite element basis function restricted to that element.

In the case N=1 the shape function (and the finite element space) is scalar, otherwise it is vector-valued. The last point is understood as follows let $\Omega_e$ be the domain of an element $ e $ and $T : \Omega_E \to \Omega_e$ the transformation from the reference element to the element e. Then the basis function $ b $ defined by $\phi$ is: $b(T(x)) = \phi(x)$ .

A ShapeFunction has the following template parameters:

C type for input coordinates x R^d
T return type for function values and derivatives
d the dimension of the reference domain
N number of components per shape function


Public Types
enum
	Dimension of the reference domain.
enum
	Number of components per shape function.
typedef C	CoordType
	Type used for the coordinates.
typedef T	ResultType
	Type used for the result values.
Public Member Functions
virtual ResultType	evaluateFunction (int comp, const FieldVector< CoordType, dim > &x) const =0
	evaluate component comp at point x
virtual ResultType	evaluateDerivative (int comp, int dir, const FieldVector< CoordType, dim > &x) const=0
	evaluate derivative of component comp in direction dir at point x
virtual int	localindex (int comp) const=0
	consecutive number of associated dof within element
virtual int	codim () const=0
	codim of associated dof
virtual int	entity () const=0
	entity (of codim) of associated dof
virtual int	entityindex () const=0
	consecutive number of dof within entity
virtual	~ShapeFunction ()
	virtual destructor

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

shapefunctions.hh

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

Detailed Description

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

Public Types

Public Member Functions

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

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