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De Rham complex families | \(\left[S_{2,k}^\square\right]_{1}\) / \(\mathcal{S}^-_{k}\Lambda^{1}(\square_d)\) |
Orders | \(1\leqslant k\) |
Reference elements | quadrilateral, hexahedron |
Polynomial set | \(\mathcal{P}_{k-1}^d \oplus \mathcal{Z}^{(41)}_{k} \oplus \mathcal{Z}^{(42)}_{k}\) (quadrilateral) \(\mathcal{P}_{k-1}^d \oplus \mathcal{Z}^{(43)}_{k} \oplus \mathcal{Z}^{(44)}_{k} \oplus \mathcal{Z}^{(45)}_{k} \oplus \mathcal{Z}^{(46)}_{k} \oplus \mathcal{Z}^{(47)}_{k}\) (hexahedron) ↓ Show polynomial set definitions ↓ |
DOFs | On each edge: tangential integral moments with an order \(k-1\) dPc space On each face: integral moments with an order \(k-3\) vector dPc space, and integral moments with \(\left\{\nabla(p)\middle|p\text{ is an order \(k-1\) monomial}\right\}\) |
Mapping | covariant Piola |
continuity | Components tangential to facets are continuous |
Categories | Vector-valued elements, H(curl) conforming elements |
FIAT | FIAT.TrimmedSerendipityCurl ↓ Show FIAT examples ↓ This implementation is correct for some of the examples below. |
Symfem | "TScurl" ↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. |
quadrilateral order 1 | ![]() (click to view basis functions) |
quadrilateral order 2 | ![]() (click to view basis functions) |
quadrilateral order 3 | ![]() (click to view basis functions) |
hexahedron order 1 | ![]() (click to view basis functions) |
hexahedron order 2 | ![]() (click to view basis functions) |
hexahedron order 3 | ![]() (click to view basis functions) |
Element added | 07 October 2021 |
Element last updated | 16 September 2023 |