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| Alternative names | vector Lagrange |
| Degrees | \(0\leqslant k\) where \(k\) is the polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | \(dk\) |
| Lagrange subdegree | \(k\) |
| Lagrange superdegree | \(k\) |
| Reference cells | quadrilateral, hexahedron |
| Finite dimensional space | \(\mathcal{Q}_{k}^d\) ↓ Show set definitions ↓ |
| DOFs | On each vertex: point evaluations in coordinate directions On each edge: point evaluations in coordinate directions On each face: point evaluations in coordinate directions On each volume: point evaluations in coordinate directions |
| Number of DOFs | interval: \(k+1\) (A000027) quadrilateral: \(2(k+1)^2\) (A001105) hexahedron: \(3(k+1)^3\) (A117642) |
| Mapping | identity |
| continuity | Function values are continuous. |
| Categories | Vector-valued elements |
| quadrilateral degree 1 | ![]() (click to view basis functions) |
| quadrilateral degree 2 | ![]() (click to view basis functions) |
| hexahedron degree 1 | ![]() (click to view basis functions) |
| hexahedron degree 2 | ![]() (click to view basis functions) |
| Element added | 30 December 2020 |
| Element last updated | 04 June 2025 |