an encyclopedia of finite element definitions
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| Abbreviated names | BDDF |
| Degrees | \(1\leqslant k\) where \(k\) is the polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(k+1\) |
| Lagrange subdegree | \(\operatorname{floor}(k/3)\) |
| Lagrange superdegree | \(k\) |
| Reference cells | hexahedron |
| Finite dimensional space | \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(8)}_{k} \oplus \mathcal{Z}^{(9)}_{k}\) ↓ Show set definitions ↓ |
| DOFs | On each facet: normal integral moments with a degree \(k\) Lagrange space On the interior of the reference cell: integral moments with a degree \(k-2\) vector Lagrange space |
| Number of DOFs | hexahedron: \((k+1)(k^2+5k+12)/2\) |
| Mapping | contravariant Piola |
| continuity | Components normal to facets are continuous |
| Categories | Vector-valued elements, H(div) conforming elements |
| hexahedron degree 1 | ![]() (click to view basis functions) |
| hexahedron degree 2 | ![]() (click to view basis functions) |
| Element added | 31 January 2021 |
| Element last updated | 04 June 2025 |