Interpolation

Ferrite.Interpolation — Type

Interpolation{ref_shape, order}()

Abstract type for interpolations defined on ref_shape (see AbstractRefShape). order corresponds to the order of the interpolation. The interpolation is used to define shape functions to interpolate a function between nodes.

The following interpolations are implemented:

Lagrange{RefLine, 1}
Lagrange{RefLine, 2}
Lagrange{RefQuadrilateral, 1}
Lagrange{RefQuadrilateral, 2}
Lagrange{RefQuadrilateral, 3}
Lagrange{RefTriangle, 1}
Lagrange{RefTriangle, 2}
Lagrange{RefTriangle, 3}
Lagrange{RefTriangle, 4}
Lagrange{RefTriangle, 5}
BubbleEnrichedLagrange{RefTriangle, 1}
CrouzeixRaviart{RefTriangle, 1}
CrouzeixRaviart{RefTetrahedron, 1}
RannacherTurek{RefQuadrilateral, 1}
RannacherTurek{RefHexahedron, 1}
Lagrange{RefHexahedron, 1}
Lagrange{RefHexahedron, 2}
Lagrange{RefTetrahedron, 1}
Lagrange{RefTetrahedron, 2}
Lagrange{RefPrism, 1}
Lagrange{RefPrism, 2}
Lagrange{RefPyramid, 1}
Lagrange{RefPyramid, 2}
Serendipity{RefQuadrilateral, 2}
Serendipity{RefHexahedron, 2}
Nedelec{RefTriangle, 1}
Nedelec{RefTriangle, 2}
Nedelec{RefQuadrilateral, 1}
Nedelec{RefTetrahedron, 1}
Nedelec{RefHexahedron, 1}
RaviartThomas{RefTriangle, 1}
RaviartThomas{RefTriangle, 2}
RaviartThomas{RefQuadrilateral, 1}
RaviartThomas{RefTetrahedron, 1}
RaviartThomas{RefHexahedron, 1}
BrezziDouglasMarini{RefTriangle, 1}

Additionally, DiscontinuousLagrange is implemented for the same reference shapes and orders as Lagrange, as well as for order = 0 on any reference shape.

Examples

julia> ip = Lagrange{RefTriangle, 2}()
Lagrange{RefTriangle, 2}()

julia> getnbasefunctions(ip)
6

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Ferrite.getnbasefunctions — Function

Ferrite.getnbasefunctions(ip::Interpolation)

Return the number of base functions for the interpolation ip.

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Ferrite.getrefdim — Method

Ferrite.getrefdim(::Interpolation)

Return the dimension of the reference element for a given interpolation.

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Ferrite.getrefshape — Function

Ferrite.getrefshape(::Interpolation)::AbstractRefShape

Return the reference element shape of the interpolation.

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Ferrite.getorder — Function

Ferrite.getorder(::Interpolation)

Return order of the interpolation.

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Implemented interpolations:

Ferrite.Lagrange — Type

Lagrange{refshape, order} <: ScalarInterpolation

Standard continuous Lagrange polynomials with equidistant node placement.

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Ferrite.Serendipity — Type

Serendipity{refshape, order} <: ScalarInterpolation

Serendipity element on hypercubes. Currently only second order variants are implemented.

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Ferrite.DiscontinuousLagrange — Type

Piecewise discontinuous Lagrange basis via Gauss-Lobatto points.

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Ferrite.BubbleEnrichedLagrange — Type

Lagrange element with bubble stabilization.

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Ferrite.CrouzeixRaviart — Type

CrouzeixRaviart{refshape, order} <: ScalarInterpolation

Classical non-conforming Crouzeix–Raviart element.

For details we refer to the original paper [10].

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Ferrite.RannacherTurek — Type

RannacherTurek{refshape, order} <: ScalarInterpolation

Classical non-conforming Rannacher-Turek element.

This element is basically the idea from Crouzeix and Raviart applied to hypercubes. For details see the original paper [11].

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