an encyclopedia of finite element definitions

# Brezzi–Douglas–Durán–Fortin

 Abbreviated names BDDF Orders $$1\leqslant k$$ Reference elements hexahedron Polynomial set $$\mathcal{P}_{k}^d \oplus \mathcal{Z}^{(8)}_{k} \oplus \mathcal{Z}^{(9)}_{k}$$↓ 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 $$k-2$$ vector Lagrange space Number of DOFs hexahedron: $$(k+1)(k^2+5k+12)/2$$ Mapping contravariant Piola continuity Components normal to facets are continuous Categories Vector-valued elements, H(div) conforming elements

## Implementations

 Symfem "BDDF"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations.

## Examples

 hexahedronorder 1 (click to view basis functions) hexahedronorder 2 (click to view basis functions)

## References

• Brezzi, Franco, Douglas, Jim, Durán, Ricardo G., and Fortin, Michel. Mixed finite elements for second order elliptic problems in three variables, Numerische Mathematik 51, 237–250, 1987. [DOI: 10.1007/BF01396752] [BibTeX]

## DefElement stats

 Element added 31 January 2021 Element last updated 16 September 2023