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Brezzi–Douglas–Durán–Fortin

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Abbreviated namesBDDF
Orders\(1\leqslant k\)
Reference elementshexahedron
Polynomial set\(\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(40)}_{k} \oplus \mathcal{Z}^{(41)}_{k}\)
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DOFsOn each facet: normal integral moments with an order \(k\) Lagrange space
On the interior of the reference element: integral moments with an order \(k-2\) vector Lagrange space
Number of DOFshexahedron: \((k+1)(k^2+5k+12)/2\)
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

Symfem"BDDF"
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Examples

hexahedron
order 1

(click to view basis functions)
hexahedron
order 2

(click to view basis functions)

References

DefElement stats

Element added31 January 2021
Element last updated02 August 2022