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Arnold–Boffi–Falk

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Abbreviated namesABF
Degrees\(0\leqslant k\)
where \(k\) is the Polynomial subdegree
Polynomial subdegree\(k\)
Polynomial superdegree\(2k+2\)
Lagrange subdegree\(k\)
Lagrange superdegree\(k+2\)
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 degree \(k\) Lagrange space
On each face: integral moments with an degree \(k\) 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

This element is implemented in Symfem .↓ Show implementation detail ↓

Examples

quadrilateral
degree 0

(click to view basis functions)
quadrilateral
degree 1

(click to view basis functions)
quadrilateral
degree 2

(click to view basis functions)

References

DefElement stats

Element added01 December 2021
Element last updated27 September 2024