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Bernstein

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Alternative namesBernstein–Bézier
Degrees\(0\leqslant k\)
where \(k\) is the Lagrange superdegree
Polynomial subdegree\(k\)
Polynomial superdegree\(k\)
Lagrange subdegree\(k\)
Lagrange superdegree\(k\)
Reference elementsinterval, triangle, tetrahedron
Polynomial set\(\mathcal{P}_{k}\)
↓ Show polynomial set definitions ↓
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

This element is implemented in FIAT , Symfem , and (legacy) UFL.↓ Show implementation detail ↓

Examples

interval
degree 1

(click to view basis functions)
interval
degree 2

(click to view basis functions)
interval
degree 3

(click to view basis functions)
triangle
degree 1

(click to view basis functions)
triangle
degree 2

(click to view basis functions)
triangle
degree 3

(click to view basis functions)

References

DefElement stats

Element added20 February 2021
Element last updated27 September 2024