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Morley–Wang–Xu
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| Degrees | interval: \(k=1\) triangle: \(1\leqslant k\leqslant 2\) tetrahedron: \(1\leqslant k\leqslant 3\) where \(k\) is the Polynomial superdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(k\) |
| Reference elements | interval, triangle, tetrahedron |
| Polynomial set | \(\mathcal{P}_{k}\) ↓ Show polynomial set definitions ↓ |
| DOFs | On each vertex: point evaluations On each edge: integrals of normal derivatives On each face: integrals of normal derivatives On each volume: integrals of normal derivatives |
| Number of DOFs | interval: \(k+1\) (A000027) triangle: \((k+1)(k+2)/2\) (A000217) tetrahedron: \((k+1)(k+2)(k+3)/6\) (A000292) |
| Mapping | identity |
| Notes | A Morley-Wang-Xu element of degree \(k\) and reference element dimension \(d\) only includes degrees of freedom on subentities of dimensions \((d - i), 1 \leqslant i \leqslant k \). |
| Categories | Scalar-valued elements |
Implementations
This element is implemented in Symfem .↓ Show implementation detail ↓Examples
| interval degree 1 |  (click to view basis functions) |
| triangle degree 1 |  (click to view basis functions) |
| triangle degree 2 |  (click to view basis functions) |
| tetrahedron degree 1 |  (click to view basis functions) |
| tetrahedron degree 2 |  (click to view basis functions) |
| tetrahedron degree 3 |  (click to view basis functions) |
References
- Wang, Ming and Xu, Jaochao. Minimal finite element spaces for 2m-th-order partial differential equations in Rn, Mathematics of computation 82(281), 25–43, 2013. [DOI: 10.1090/S0025-5718-2012-02611-1] [BibTeX]
DefElement stats
| Element added | 08 June 2021 |
| Element last updated | 24 October 2024 |