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Alternative names | Bernstein–Bézier |
Degrees | \(0\leqslant k\) where \(k\) is the Lagrange superdegree |
Polynomial subdegree | \(k\) |
Polynomial superdegree | \(k\) |
Lagrange subdegree | \(k\) |
Lagrange superdegree | \(k\) |
Reference elements | interval, triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k}\) ↓ Show polynomial set definitions ↓ |
DOFs | On 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 DOFs | interval: \(k+1\) (A000027) triangle: \((k+1)(k+2)/2\) (A000217) tetrahedron: \((k+1)(k+2)(k+3)/6\) (A000292) |
Mapping | identity |
continuity | Function values are continuous. |
Categories | Scalar-valued elements |
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) |
Element added | 20 February 2021 |
Element last updated | 27 September 2024 |