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Exterior calculus names | \(\mathcal{P}_{k}\Lambda^{d-1}(\Delta_d)\) |
Cockburn–fu names | \(\left[S_{1,k}^\unicode{0x25FA}\right]_{d-1}\) |
Abbreviated names | BDM |
Orders | \(1\leqslant k\) |
Reference elements | triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k}^d\) ↓ Show polynomial set definitions ↓ |
DOFs | On each facet: normal integral moments with an order \(k\) Lagrange space On the interior of the reference element: integral moments with an order \(k-1\) Nédélec (first kind) space |
Number of DOFs | triangle: \((k+1)(k+2)\) (A002378) tetrahedron: \((k+1)(k+2)(k+3)/2\) (A027480) |
Mapping | contravariant Piola |
continuity | Components normal to facets are continuous |
Categories | Vector-valued elements, H(div) conforming elements |
Basix | basix.ElementFamily.BDM ↓ Show Basix examples ↓ |
Symfem | "N2div" ↓ Show Symfem examples ↓ |
UFL | "BDM" ↓ Show UFL examples ↓ |
triangle order 1 | ![]() (click to view basis functions) |
triangle order 2 | ![]() (click to view basis functions) |
tetrahedron order 1 | ![]() (click to view basis functions) |
tetrahedron order 2 | ![]() (click to view basis functions) |
Element added | 30 December 2020 |
Element last updated | 02 August 2022 |