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Fortin–Soulie
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| Abbreviated names | FS |
| Degrees | \(k=2\) where \(k\) is the polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(k\) |
| Reference cells | triangle |
| Finite dimensional space | \(\mathcal{P}_{k}\) ↓ Show set definitions ↓ |
| DOFs | On each facet: point evaluation at two points (but only one point on one of the edges) On the interior of the reference cell: point evaluation at midpoint |
| Number of DOFs | triangle: \(6\) |
| Mapping | identity |
| continuity | Discontinuous. |
| Categories | Scalar-valued elements |
Implementations
This element is implemented in Symfem .↓ Show implementation detail ↓Examples
| triangle degree 2 |  (click to view basis functions) |
References
- Fortin, Michel and Soulie, M. A non‐conforming piecewise quadratic finite element on triangles, International Journal for Numerical Methods in Engineering 19, 505–520, 1983. [DOI: 10.1002/nme.1620190405] [BibTeX]
DefElement stats
| Element added | 06 March 2021 |
| Element last updated | 04 June 2025 |