dune-localfunctions 2.10
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Public Types | Public Member Functions | Static Public Member Functions | List of all members
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
DType to represent the field in the domain.
RType to represent the field in the range.
dimdimension of the reference elements, must be >= 2.
orderorder 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
sEdge 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: