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Bernstein

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Alternative namesBernstein–Bézier
Orders\(0\leqslant k\)
Reference elementsinterval, triangle, tetrahedron
Polynomial set\(\mathcal{P}_{k}\)
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DOFsOn each vertex: point evaluations
On each edge: evaluation of Bernstein coefficients
On each face: evaluation of Bernstein coefficients
On each volume: evaluation of Bernstein coefficients
Number of DOFsinterval: \(k+1\) (A000027)
triangle: \((k+1)(k+2)/2\) (A000217)
tetrahedron: \((k+1)(k+2)(k+3)/6\) (A000292)
Mappingidentity
continuityFunction values are continuous.
CategoriesScalar-valued elements

Implementations

Symfem"Bernstein"
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UFL"Bernstein"
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Examples

interval
order 1
(click to view basis functions)
interval
order 2
(click to view basis functions)
interval
order 3
(click to view basis functions)
triangle
order 1
(click to view basis functions)
triangle
order 2
(click to view basis functions)
triangle
order 3
(click to view basis functions)

References

DefElement stats

Element added20 February 2021
Element last updated02 August 2022