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Gauss–Legendre
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| Degrees | \(0\leqslant k\) where \(k\) is the Lagrange superdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(dk\) |
| Lagrange subdegree | \(k\) |
| Lagrange superdegree | \(k\) |
| Reference elements | interval, quadrilateral, hexahedron |
| Polynomial set | \(\mathcal{Q}_{k}\) ↓ Show polynomial set definitions ↓ |
| DOFs | On each vertex: point evaluations On each edge: point evaluations at Gauss–Legendre points On each face: point evaluations at Gauss–Legendre points On each volume: point evaluations at Gauss–Legendre points |
| Number of DOFs | interval: \(k+1\) (A000027) quadrilateral: \((k+1)^2\) (A000290) hexahedron: \((k+1)^3\) (A000578) |
| Mapping | identity |
| continuity | Function values are continuous. |
| Categories | Scalar-valued elements |
Implementations
This element is implemented in Symfem .↓ Show implementation detail ↓Examples
| interval degree 1 |  (click to view basis functions) |
| interval degree 2 |  (click to view basis functions) |
| quadrilateral degree 1 |  (click to view basis functions) |
| quadrilateral degree 2 |  (click to view basis functions) |
DefElement stats
| Element added | 20 February 2021 |
| Element last updated | 27 September 2024 |