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Alternative names | vector Lagrange |
Orders | \(0\leqslant k\) |
Reference elements | quadrilateral, hexahedron |
Polynomial set | \(\mathcal{Q}_{k}^d\) ↓ Show polynomial 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 |
Basix.UFL | basix.ElementFamily.P, lagrange_variant=basix.LagrangeVariant.equispaced, shape=(dim,) ↓ Show Basix.UFL examples ↓ This implementation is correct for all the examples below. |
Symfem | "vector Q" ↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. |
(legacy) UFL | "Q" ↓ Show (legacy) UFL examples ↓ |
quadrilateral order 1 | (click to view basis functions) |
quadrilateral order 2 | (click to view basis functions) |
hexahedron order 1 | (click to view basis functions) |
hexahedron order 2 | (click to view basis functions) |
Element added | 30 December 2020 |
Element last updated | 29 September 2023 |