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Conforming Crouzeix–Raviart
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| Abbreviated names | conforming CR |
| Degrees | \(1\leqslant k\) where \(k\) is the Polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(k+1\) |
| Reference elements | triangle |
| Polynomial set | \(\mathcal{P}_{k} \oplus \mathcal{Z}^{(12)}_{k}\) ↓ Show polynomial set definitions ↓ |
| DOFs | On each vertex: points evaluation On each edge: point evaluations On each face: point evaluations |
| Number of DOFs | triangle: \(k(k+5)/2\) |
| Mapping | identity |
| continuity | Discontinuous. |
| Categories | Scalar-valued elements |
Implementations
This element is implemented in Symfem .↓ Show implementation detail ↓Examples
| triangle degree 1 |  (click to view basis functions) |
| triangle degree 2 |  (click to view basis functions) |
| triangle degree 3 |  (click to view basis functions) |
| triangle degree 4 |  (click to view basis functions) |
| triangle degree 5 |  (click to view basis functions) |
References
- Crouzeix, Michel and Raviart, Pierre-Arnaud. Conforming and nonconforming finite element methods for solving the stationary Stokes equations, Revue Française d'Automatique, Informatique et Recherche Opérationnelle 3, 33–75, 1973. [DOI: 10.1051/m2an/197307R300331] [BibTeX]
DefElement stats
| Element added | 04 July 2021 |
| Element last updated | 27 September 2024 |