an encyclopedia of finite element definitions

# Vector Q

 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

## Implementations

 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 ↓

## Examples

 quadrilateralorder 1 (click to view basis functions) quadrilateralorder 2 (click to view basis functions) hexahedronorder 1 (click to view basis functions) hexahedronorder 2 (click to view basis functions)

## DefElement stats

 Element added 30 December 2020 Element last updated 29 September 2023