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De Rham complex families | \(\left[S_{2,k}^\square\right]_{1}\) or \(\mathcal{S}^-_{k}\Lambda^{1}(\square_d)\) |
Degrees | \(0\leqslant k\) where \(k\) is the Polynomial subdegree |
Polynomial subdegree | \(k\) |
Polynomial superdegree | \(k+d-1\) |
Lagrange subdegree | \(\operatorname{floor}((k+d)/(d+1))\) |
Lagrange superdegree | \(k+1\) |
Reference elements | quadrilateral, hexahedron |
Polynomial set | \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(40)}_{k+1} \oplus \mathcal{Z}^{(41)}_{k+1}\) (quadrilateral) \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(42)}_{k+1} \oplus \mathcal{Z}^{(43)}_{k+1} \oplus \mathcal{Z}^{(44)}_{k+1} \oplus \mathcal{Z}^{(45)}_{k} \oplus \mathcal{Z}^{(46)}_{k+1}\) (hexahedron) ↓ Show polynomial set definitions ↓ |
DOFs | On each edge: tangential integral moments with a degree \(k\) dPc space On each face: integral moments with a degree \(k-2\) vector dPc space, and integral moments with \(\left\{\nabla(p)\middle|p\text{ is a degree \(k\) monomial}\right\}\) |
Mapping | covariant Piola |
continuity | Components tangential to facets are continuous |
Categories | Vector-valued elements, H(curl) conforming elements |
quadrilateral degree 0 | ![]() (click to view basis functions) |
quadrilateral degree 1 | ![]() (click to view basis functions) |
quadrilateral degree 2 | ![]() (click to view basis functions) |
hexahedron degree 0 | ![]() (click to view basis functions) |
hexahedron degree 1 | ![]() (click to view basis functions) |
hexahedron degree 2 | ![]() (click to view basis functions) |
Element added | 07 October 2021 |
Element last updated | 31 March 2025 |