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Crouzeix–Falk
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| Abbreviated names | CF |
| Degrees | \(k=3\) where \(k\) is the Polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(k\) |
| Reference cells | triangle |
| Polynomial set | \(\mathcal{P}_{k}\) ↓ Show polynomial set definitions ↓ |
| DOFs | On each facet: point evaluation at three points On the interior of the reference cell: point evaluation at midpoint |
| Number of DOFs | triangle: \(10\) |
| Mapping | identity |
| continuity | Discontinuous. |
| Categories | Scalar-valued elements |
Implementations
This element is implemented in Symfem .↓ Show implementation detail ↓Examples
| triangle degree 3 |  (click to view basis functions) |
References
- Crouzeix, Michel and Falk, Richard S. Nonconforming finite elements for the Stokes problem, Mathematics of Computation 52, 437–456, 1989. [DOI: 10.2307/2008475] [BibTeX]
DefElement stats
| Element added | 06 March 2021 |
| Element last updated | 04 June 2025 |