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Enriched Galerkin
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| Abbreviated names | EG |
| Degrees | \(1\leqslant k\) where \(k\) is the Lagrange superdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | interval: \(k\) triangle: \(k\) tetrahedron: \(k\) quadrilateral: \(dk\) hexahedron: \(dk\) |
| 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: \((k+1)(k+2)(2k+3)/6 + 1\) |
| 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 |