an encyclopedia of finite element definitions
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Abbreviated names | BDDF |
Degrees | \(1\leqslant k\) where \(k\) is the Lagrange superdegree |
Polynomial subdegree | \(k\) |
Polynomial superdegree | \(k+1\) |
Lagrange subdegree | \(\operatorname{floor}(k/3)\) |
Lagrange superdegree | \(k\) |
Reference elements | hexahedron |
Polynomial set | \(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(8)}_{k} \oplus \mathcal{Z}^{(9)}_{k}\) ↓ Show polynomial set definitions ↓ |
DOFs | On each facet: normal integral moments with an degree \(k\) Lagrange space On the interior of the reference element: integral moments with an 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 | 27 September 2024 |