an encyclopedia of finite element definitions

# Vector dPc

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 Orders $$0\leqslant k$$ Reference elements interval, quadrilateral, hexahedron Polynomial set $$\mathcal{P}_{k}^d$$↓ Show polynomial set definitions ↓ DOFs On the interior of the reference element: point evaluations Number of DOFs quadrilateral: $$(k+1)(k+2)$$ (A002378)hexahedron: $$(k+1)(k+2)(k+3)/2$$ (A027480) Mapping identity continuity Discontinuous. Categories Scalar-valued elements

## Implementations

 Basix.UFL basix.ElementFamily.DPC, discontinuous=True, dpc_variant=basix.DPCVariant.simplex_equispaced, shape=(dim,)↓ Show Basix.UFL examples ↓ This implementation is correct for all the examples below. Symfem "vector dPc"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. (legacy) UFL "DPC"↓ Show (legacy) UFL examples ↓

## Examples

 quadrilateralorder 1 (click to view basis functions) quadrilateralorder 2 (click to view basis functions) quadrilateralorder 3 (click to view basis functions) hexahedronorder 1 (click to view basis functions) hexahedronorder 2 (click to view basis functions)

## DefElement stats

 Element added 30 March 2021 Element last updated 29 September 2023