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Brezzi–Douglas–Fortin–Marini

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Abbreviated namesBDFM
Orders\(1\leqslant k\)
Reference elementstriangle, quadrilateral, tetrahedron, hexahedron
Polynomial set\(\mathcal{Z}^{(51)}_{k}\)
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DOFsOn 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 DOFstriangle: \(k(k+2)\)
quadrilateral: \(k(k+3)\) (A028552)
tetrahedron: \(k(k+1)(k+3)/2\)
hexahedron: \(k(k+1)(k+5)/2\)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Symfem"BDFM"
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UFL"BDFM" (triangle, tetrahedron)
↓ Show UFL examples ↓

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)

References

DefElement stats

Element added30 January 2021
Element last updated02 August 2022