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Wu–Xu

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Ordersinterval: \(k=2\)
triangle: \(k=3\)
tetrahedron: \(k=4\)
Reference elementsinterval, triangle, tetrahedron
Polynomial set\(\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(21)}_{k}\) (interval)
\(\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(22)}_{k}\) (triangle)
\(\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(23)}_{k}\) (tetrahedron)
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DOFsOn each vertex: point evaluations
On each edge: integrals of normal derivatives
On each face: integrals of normal derivatives
On each volume: integrals of normal derivatives
Number of DOFsinterval: \(4\)
triangle: \(12\)
tetrahedron: \(38\)
Mappingidentity
continuityFunction values are continuous.
CategoriesScalar-valued elements

Implementations

Symfem"Wu-Xu"
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Examples

interval
order 2

(click to view basis functions)
triangle
order 3

(click to view basis functions)
tetrahedron
order 4

(click to view basis functions)

References

DefElement stats

Element added08 June 2021
Element last updated02 August 2022