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Alfeld–Sorokina
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| De Rham complex families | \(\mathrm{C}_d^0\mathrm{P}^2\mathrm{\Lambda}^1(\mathcal{R})\) |
| Degrees | \(k=2\) |
| Reference cells | triangle |
| DOFs | On each vertex: point evaluations in coordinate directions, and point evaulations of divergence On each edge: points evaluations in coordinate directions |
| Number of DOFs | triangle: \(15\) |
| Number of DOFs on subentities | vertices: \(3\) edges: \(2\) faces: \(0\) |
| Mapping | contravariant Piola |
| continuity | Function values and divergence are continuous. |
| Categories | Vector-valued elements, Macro elements |
Implementations
This element is implemented in FIAT and Symfem .↓ Show implementation detail ↓Examples
| triangle degree 2 |  (click to view basis functions) |
References
- Alfeld, Peter and Sorokina, Tatyana. Linear differential operators on bivariate spline spaces and spline vector fields, BIT Numerical Mathematics 56, 15–32, 2016. [DOI: 10.1007/s10543-015-0557-x] [BibTeX]
DefElement stats
| Element added | 01 June 2023 |
| Element last updated | 04 June 2025 |