dune-localfunctions 2.10
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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. | |
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
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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.
D | Type to represent the field in the domain. |
R | Type to represent the field in the range. |
dim | Dimension of the domain. |
using Dune::SimplexP1BubbleLocalFiniteElement< D, R, dim >::LocalBasisType = SimplexP1BubbleLocalBasis<D,R,dim> |
Type of the local basis.
using Dune::SimplexP1BubbleLocalFiniteElement< D, R, dim >::LocalCoefficientsType = SimplexP1BubbleLocalCoefficients<dim> |
Type of the local coefficients.
using Dune::SimplexP1BubbleLocalFiniteElement< D, R, dim >::LocalInterpolationType = SimplexP1BubbleLocalInterpolation<LocalBasisType> |
Type of the local interpolation.
using Dune::SimplexP1BubbleLocalFiniteElement< D, R, dim >::Traits = LocalFiniteElementTraits<LocalBasisType,LocalCoefficientsType,LocalInterpolationType> |
Traits type that specifies the local basis, coefficients, and interpolation type.
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Returns the local basis, i.e., the set of shape functions.
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inline |
Returns the assignment of the degrees of freedom to the element subentities.
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inline |
Returns object that evaluates degrees of freedom.
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inlinestaticconstexprnoexcept |
Returns the number of shape functions in this finite-element.
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inlinestaticconstexprnoexcept |
Returns the type of the geometry the finite-element is attached to.