Dune::SimplexP1BubbleLocalFiniteElement< D, R, dim > Class Template Reference

Linear Lagrange functions enriched with an element bubble function. More...

#include <dune/localfunctions/enriched/simplexp1bubble.hh>

Public Types
using	LocalBasisType = SimplexP1BubbleLocalBasis< D, R, dim >
	Type of the local basis.
using	LocalCoefficientsType = SimplexP1BubbleLocalCoefficients< dim >
	Type of the local coefficients.
using	LocalInterpolationType = SimplexP1BubbleLocalInterpolation< LocalBasisType >
	Type of the local interpolation.
using	Traits = LocalFiniteElementTraits< LocalBasisType, LocalCoefficientsType, LocalInterpolationType >
	Traits type that specifies the local basis, coefficients, and interpolation type.

Public Member Functions
const LocalBasisType &	localBasis () const
	Returns the local basis, i.e., the set of shape functions.
const LocalCoefficientsType &	localCoefficients () const
	Returns the assignment of the degrees of freedom to the element subentities.
const LocalInterpolationType &	localInterpolation () const
	Returns object that evaluates degrees of freedom.

Static Public Member Functions
static constexpr std::size_t	size () noexcept
	Returns the number of shape functions in this finite-element.
static constexpr GeometryType	type () noexcept
	Returns the type of the geometry the finite-element is attached to.

Detailed Description

template<class D, class R, int dim>
class Dune::SimplexP1BubbleLocalFiniteElement< D, R, dim >

Linear Lagrange functions enriched with an element bubble function.

The set of basis functions contains the classical Lagrange basis functions of order 1, i.e., the barycentric coordinates, and a single element "bubble" function that vanishes on all faces of the element. The bubble function is simply defined as the product of all linear basis functions and thus has polynomial order dim+1.

A classical example where this kind of basis is used in the discretization of the Stokes equation with the stable mixed-element called MINI element, see

Arnold, D.N., Brezzi, F. and Fortin, M. A stable finite element for the Stokes equations. Calcolo 21, 337-344 (1984). doi: 10.1007/BF02576171

The velocity field is discretized with continuous piecewise linear functions enriched by a bubble function.

Note

The implementation here is restricted to simplex elements.

Template Parameters

D	Type to represent the field in the domain.
R	Type to represent the field in the range.
dim	Dimension of the domain.

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

• dune/localfunctions/enriched/simplexp1bubble.hh