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Exterior calculus names | \(\mathcal{S}_{k}\Lambda^{0}(\square_d)\), \(\mathcal{S}^-_{k-d}\Lambda^{0}(\square_d)\) |
Cockburn–fu names | \(\left[S_{1,k}^\square\right]_{0}\), \(\left[S_{2,k-d}^\square\right]_{0}\) |
Abbreviated names | S |
Orders | \(1\leqslant k\) |
Reference elements | interval, quadrilateral, hexahedron |
Polynomial set | \(\mathcal{P}_{k} \oplus \mathcal{X}_{k}\) ↓ Show polynomial set definitions ↓ |
DOFs | On each vertex: point evaluations On each edge: integral moments with an order \(k-2\) dPc space On each face: integral moments with an order \(k-4\) dPc space On each volume: integral moments with an order \(k-6\) dPc space |
Number of DOFs | interval: \(k+1\) (A000027) quadrilateral: \(\begin{cases}4&k=1\\k(k+3)/2+3&k>1\end{cases}\) (A340266) hexahedron: \(\begin{cases}12k-4&k=1,2,3\\3k^2-3k+14&k=4,5\\k(k-1)(k+1)/6+k^2+5k+4&k>6\end{cases}\) |
Mapping | identity |
continuity | Function values are continuous. |
Categories | Scalar-valued elements |
Basix | basix.ElementFamily.serendipity, ..., basix.LagrangeVariant.equispaced ↓ Show Basix examples ↓ |
Symfem | "serendipity" ↓ Show Symfem examples ↓ |
UFL | "S" ↓ Show UFL examples ↓ |
interval order 1 | ![]() (click to view basis functions) |
interval order 2 | ![]() (click to view basis functions) |
interval order 3 | ![]() (click to view basis functions) |
quadrilateral order 1 | ![]() (click to view basis functions) |
quadrilateral order 2 | ![]() (click to view basis functions) |
quadrilateral order 3 | ![]() (click to view basis functions) |
Element added | 02 January 2021 |
Element last updated | 02 August 2022 |