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Alternative names | Raviart–Thomas cubical H(div) (quadrilateral), Nédélec cubical H(div) (hexahedron) |
De Rham complex families | \(\left[S_{4,k}^\square\right]_{d-1}\) / \(\mathcal{Q}^-_{k}\Lambda^{d-1}(\square_d)\) |
Abbreviated names | RTcf (quadrilateral), Ncf (hexahedron) |
Orders | \(1\leqslant k\) |
Reference elements | quadrilateral, hexahedron |
Polynomial set | \(\mathcal{Q}_{k-1}^d \oplus \mathcal{Z}^{(23)}_{k}\) (quadrilateral) \(\mathcal{Q}_{k}^d \oplus \mathcal{Z}^{(23)}_{k}\) (hexahedron) ↓ Show polynomial set definitions ↓ |
DOFs | On each facet: normal integral moments with an order \(k-1\) Lagrange space On the interior of the reference element: integral moments with an order \(k-1\) Nédélec (first kind) space |
Number of DOFs | quadrilateral: \(2k(k+1)\) (A046092) hexahedron: \(3k^2(k+1)\) (A270205) |
Mapping | contravariant Piola |
continuity | Components normal to facets are continuous |
Categories | Vector-valued elements, H(div) conforming elements |
Symfem | "Qdiv" ↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. |
(legacy) UFL | "RTCF" (quadrilateral)"NCF" (hexahedron)↓ Show (legacy) UFL examples ↓ |
quadrilateral order 1 | ![]() (click to view basis functions) |
quadrilateral order 2 | ![]() (click to view basis functions) |
hexahedron order 1 | ![]() (click to view basis functions) |
hexahedron order 2 | ![]() (click to view basis functions) |
Element added | 31 December 2020 |
Element last updated | 16 September 2023 |