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Arnold–Boffi–Falk

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Abbreviated namesABF
Orders\(0\leqslant k\)
Reference elementsquadrilateral
Polynomial set\(\mathcal{Z}^{(0)}_{k} \oplus \mathcal{Z}^{(1)}_{k}\)
↓ Show polynomial set definitions ↓
DOFsOn each edge: normal integral moments with an order \(k\) Lagrange space
On each face: integral moments with an order \(k\) Nédélec (first kind) space,
integral moments of the divergence with \(x^{k+1}y^q\) for q=0,1,...,k, and integral moments of the divergence with \(x^qy^{k+1}\) for q=0,1,...,k
Mappingcontravariant Piola
continuityComponents normal to facets are continuous
CategoriesVector-valued elements, H(div) conforming elements

Implementations

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

Examples

quadrilateral
order 0

(click to view basis functions)
quadrilateral
order 1

(click to view basis functions)
quadrilateral
order 2

(click to view basis functions)

References

DefElement stats

Element added01 December 2021
Element last updated03 January 2024