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Enriched Galerkin

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Abbreviated names	EG
Degrees	$1 ⩽ k$ where $k$ is the Lagrange superdegree
Polynomial subdegree	$k$
Polynomial superdegree	interval: $k$ triangle: $k$ tetrahedron: $k$ quadrilateral: $d k$ hexahedron: $d k$
Lagrange subdegree	$k$
Lagrange superdegree	$k$
Reference elements	interval, triangle, tetrahedron, quadrilateral, hexahedron, prism, pyramid
Number of DOFs	interval: $k + 2$ (A000027) triangle: $(k + 1) (k + 2) / 2 + 1$ tetrahedron: $(k + 1) (k + 2) (k + 3) / 6 + 1$ quadrilateral: $(k + 1)^{2} + 1$ hexahedron: $(k + 1)^{3} + 1$ prism: $(k + 1)^{2} (k + 2) / 2 + 1$ pyramid: $(k + 1) (k + 2) (2 k + 3) / 6 + 1$
Mapping	identity
continuity	Discontinuous.
Notes	This is a continuous Lagrange element enriched with a discontinuous piecewise constant element.
Categories	Scalar-valued elements

Implementations

This element is implemented in Symfem .↓ Show implementation detail ↓

Examples

interval degree 1	(click to view basis functions)
interval degree 2	(click to view basis functions)
triangle degree 1	(click to view basis functions)
triangle degree 2	(click to view basis functions)
quadrilateral degree 1	(click to view basis functions)
quadrilateral degree 2	(click to view basis functions)
tetrahedron degree 1	(click to view basis functions)
tetrahedron degree 2	(click to view basis functions)
hexahedron degree 1	(click to view basis functions)
hexahedron degree 2	(click to view basis functions)

References

Sun, Shuyu and Liu, Jiangguo. A locally conservative finite element method based on piecewise constant enrichment of the continuous Galerkin method, SIAM Journal on Scientific Computing 31(4), 2528–2548, 2009. [DOI: 10.1137/080722953] [BibTeX]

DefElement stats

Element added	05 March 2023
Element last updated	27 September 2024