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Brezzi–Douglas–Marini

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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 namesBDM
Orders\(1\leqslant k\)
Reference elementstriangle, tetrahedron
Polynomial set\(\mathcal{P}_{k}^d\)
↓ Show polynomial set definitions ↓
DOFsOn 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 DOFstriangle: \((k+1)(k+2)\) (A002378)
tetrahedron: \((k+1)(k+2)(k+3)/2\) (A027480)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Basixbasix.ElementFamily.BDM
↓ Show Basix examples ↓
Symfem"N2div"
↓ Show Symfem examples ↓
UFL"BDM"
↓ Show UFL examples ↓

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)

References

DefElement stats

Element added30 December 2020
Element last updated02 August 2022