dune-localfunctions 2.10
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Public Types | Public Member Functions | Static Public Member Functions | List of all members
Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k > Class Template Reference

Nédélec elements of the first kind for cube elements. More...

#include <dune/localfunctions/nedelec/nedelec1stkindcube.hh>

Public Types

using Traits = LocalFiniteElementTraits< Impl::Nedelec1stKindCubeLocalBasis< D, R, dim, k >, Impl::Nedelec1stKindCubeLocalCoefficients< dim, k >, Impl::Nedelec1stKindCubeLocalInterpolation< Impl::Nedelec1stKindCubeLocalBasis< D, R, dim, k > > >
 

Public Member Functions

 Nedelec1stKindCubeLocalFiniteElement ()=default
 Default constructor.
 
 Nedelec1stKindCubeLocalFiniteElement (std::bitset< power(2, dim-1) *dim > s)
 Constructor with explicitly given edge orientations.
 
const Traits::LocalBasisTypelocalBasis () const
 
const Traits::LocalCoefficientsTypelocalCoefficients () const
 
const Traits::LocalInterpolationTypelocalInterpolation () const
 

Static Public Member Functions

static constexpr unsigned int size ()
 
static constexpr GeometryType type ()
 

Detailed Description

template<class D, class R, int dim, int k>
class Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >

Nédélec elements of the first kind for cube elements.

These elements have been described in :

J.C. Nédélec, "Mixed finite elements in R^3", Numer.Math., 35(3):315-341,1980. DOI: http://dx.doi.org/10.1007/BF01396415

The order count starts at '1'. This is the counting used, e.g., by Nédélec himself, and by Kirby, Logg, Rognes, Terrel, "Common and unusual finite elements", https://doi.org/10.1007/978-3-642-23099-8_3

Note
These shape functions are implemented for the reference cube only! The transformation to other cubes has to be done by the user.
Template Parameters
DNumber type used for domain coordinates
RNumber type use for shape function values
dimDimension of the domain
kOrder of the Nedelec finite element (lowest is 1)

Member Typedef Documentation

◆ Traits

template<class D , class R , int dim, int k>
using Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::Traits = LocalFiniteElementTraits<Impl::Nedelec1stKindCubeLocalBasis<D,R,dim,k>, Impl::Nedelec1stKindCubeLocalCoefficients<dim,k>, Impl::Nedelec1stKindCubeLocalInterpolation<Impl::Nedelec1stKindCubeLocalBasis<D,R,dim,k> > >

Constructor & Destructor Documentation

◆ Nedelec1stKindCubeLocalFiniteElement() [1/2]

template<class D , class R , int dim, int k>
Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::Nedelec1stKindCubeLocalFiniteElement ( )
default

Default constructor.

◆ Nedelec1stKindCubeLocalFiniteElement() [2/2]

template<class D , class R , int dim, int k>
Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::Nedelec1stKindCubeLocalFiniteElement ( std::bitset< power(2, dim-1) *dim >  s)
inline

Constructor with explicitly given edge orientations.

Parameters
sEdge orientation indicator

Member Function Documentation

◆ localBasis()

template<class D , class R , int dim, int k>
const Traits::LocalBasisType & Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::localBasis ( ) const
inline

◆ localCoefficients()

template<class D , class R , int dim, int k>
const Traits::LocalCoefficientsType & Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::localCoefficients ( ) const
inline

◆ localInterpolation()

template<class D , class R , int dim, int k>
const Traits::LocalInterpolationType & Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::localInterpolation ( ) const
inline

◆ size()

template<class D , class R , int dim, int k>
static constexpr unsigned int Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::size ( )
inlinestaticconstexpr

◆ type()

template<class D , class R , int dim, int k>
static constexpr GeometryType Dune::Nedelec1stKindCubeLocalFiniteElement< D, R, dim, k >::type ( )
inlinestaticconstexpr

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