an encyclopedia of finite element definitions

# Vector Lagrange

 Orders $$0\leqslant k$$ Reference elements triangle, tetrahedron Polynomial set $$\mathcal{P}_{k}^d$$↓ 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 triangle: $$(k+1)(k+2)$$ (A002378)tetrahedron: $$(k+1)(k+2)(k+3)/2$$ (A027480) Mapping identity continuity Function values are continuous. Categories Vector-valued elements

## Implementations

 Basix.UFL basix.ElementFamily.P, lagrange_variant=basix.LagrangeVariant.equispaced, rank=, shape=(dim,)↓ Show Basix.UFL examples ↓ This implementation is correct for all the examples below. Symfem "vector Lagrange"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. (legacy) UFL "Lagrange"↓ Show (legacy) UFL examples ↓

## Examples

 triangleorder 1 (click to view basis functions) triangleorder 2 (click to view basis functions) tetrahedronorder 1 (click to view basis functions) tetrahedronorder 2 (click to view basis functions)

## DefElement stats

 Element added 30 December 2020 Element last updated 29 September 2023