Dune::BDFMCubeLocalFiniteElement< D, R, dim, order > Class Template Reference

Brezzi-Douglas-Fortin-Marini finite elements for cubes. More...

#include <dune/localfunctions/brezzidouglasfortinmarini/bdfmcube.hh>

Public Types
using	Traits = LocalFiniteElementTraits< LocalBasis, LocalCoefficients, LocalInterpolation >

Public Member Functions
	BDFMCubeLocalFiniteElement ()
	Standard constructor.
	BDFMCubeLocalFiniteElement (std::bitset< 2 *dim > s)
	Make set number s, where 0 <= s < 2^(2*dim)
auto	localBasis () const -> const LocalBasis &
auto	localCoefficients () const -> const LocalCoefficients &
auto	localInterpolation () const -> const LocalInterpolation &
unsigned int	size () const
	Number of shape functions in this finite element.

Static Public Member Functions
static constexpr auto	type () -> GeometryType

Detailed Description

template<class D, class R, unsigned int dim, unsigned int order>
class Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >

Brezzi-Douglas-Fortin-Marini finite elements for cubes.

Brezzi-Douglas-Fortin-Marini (BDFM) finite elements are reduced Brezzi-Douglas-Marini (BDM) finite elements, where the order of the normal traces is lowered by one.

On a quadrilateral K the BDFM element is given by

\(BDFM_k = (P_k(K)\setminus\{y^k\})\times(P_k(K)\setminus\{x^k\})\quad(k\geq1)\)

The BDFM1 element is identical to the RT0 element.

For further reading see Brezzi, Fortin "Mixed and Hybrid Finite Element Methods" (1991), Chapter III Section 3

Template Parameters

D	Type to represent the field in the domain.
R	Type to represent the field in the range.
dim	dimension of the reference elements, must be >= 2.
order	order of the element, must be >= 1.

Member Typedef Documentation

Traits

template<class D , class R , unsigned int dim, unsigned int order>

using Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::Traits = LocalFiniteElementTraits<LocalBasis, LocalCoefficients, LocalInterpolation >

Constructor & Destructor Documentation

BDFMCubeLocalFiniteElement() [1/2]

template<class D , class R , unsigned int dim, unsigned int order>

Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::BDFMCubeLocalFiniteElement ( )

inline

Standard constructor.

BDFMCubeLocalFiniteElement() [2/2]

template<class D , class R , unsigned int dim, unsigned int order>

Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::BDFMCubeLocalFiniteElement ( std::bitset< 2 *dim >  s )

inline

Make set number s, where 0 <= s < 2^(2*dim)

Parameters

s	Edge orientation indicator

Member Function Documentation

localBasis()

template<class D , class R , unsigned int dim, unsigned int order>

auto Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::localBasis ( ) const -> const LocalBasis&

inline

localCoefficients()

template<class D , class R , unsigned int dim, unsigned int order>

auto Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::localCoefficients ( ) const -> const LocalCoefficients&

inline

localInterpolation()

template<class D , class R , unsigned int dim, unsigned int order>

auto Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::localInterpolation ( ) const -> const LocalInterpolation&

inline

size()

template<class D , class R , unsigned int dim, unsigned int order>

unsigned int Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::size ( ) const

inline

Number of shape functions in this finite element.

type()

template<class D , class R , unsigned int dim, unsigned int order>

static constexpr auto Dune::BDFMCubeLocalFiniteElement< D, R, dim, order >::type ( ) -> GeometryType

inlinestaticconstexpr

---

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

• bdfmcube.hh