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Abbreviated names | BDFM |
Orders | \(1\leqslant k\) |
Reference elements | triangle, quadrilateral, tetrahedron, hexahedron |
Polynomial set | \(\mathcal{Z}^{(10)}_{k}\) ↓ 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 \(k-2\) vector Lagrange space |
Number of DOFs | triangle: \(k(k+2)\) quadrilateral: \(k(k+3)\) (A028552) tetrahedron: \(k(k+1)(k+3)/2\) hexahedron: \(k(k+1)(k+5)/2\) |
Mapping | contravariant Piola |
continuity | Components normal to facets are continuous |
Categories | Vector-valued elements, H(div) conforming elements |
FIAT | FIAT.BrezziDouglasFortinMarini ↓ Show FIAT examples ↓ This implementation is incorrect for this element. |
Symfem | "BDFM" ↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. |
(legacy) UFL | "BDFM" ↓ Show (legacy) UFL examples ↓ |
triangle order 1 | ![]() (click to view basis functions) |
triangle order 2 | ![]() (click to view basis functions) |
quadrilateral order 1 | ![]() (click to view basis functions) |
quadrilateral order 2 | ![]() (click to view basis functions) |
tetrahedron order 2 | ![]() (click to view basis functions) |
hexahedron order 2 | ![]() (click to view basis functions) |
Element added | 30 January 2021 |
Element last updated | 16 September 2023 |