an encyclopedia of finite element definitions

# DPc

 Alternative names discontinuous polynomial cubical De Rham complex families $$\left[S_{1,k}^\square\right]_{d}$$ / $$\mathcal{S}_{k}\Lambda^{d}(\square_d)$$, $$\left[S_{2,k}^\square\right]_{d}$$ / $$\mathcal{S}^-_{k}\Lambda^{d}(\square_d)$$ Orders $$0\leqslant k$$ Reference elements interval, quadrilateral, hexahedron Polynomial set $$\mathcal{P}_{k}$$↓ Show polynomial set definitions ↓ DOFs On the interior of the reference element: point evaluations Number of DOFs interval: $$k+1$$ (A000027)quadrilateral: $$(k+1)(k+2)/2$$ (A000217)hexahedron: $$(k+1)(k+2)(k+3)/6$$ (A000292) Mapping identity continuity Discontinuous. Categories Scalar-valued elements

## Implementations

 Basix basix.ElementFamily.DPC, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True↓ Show Basix examples ↓ This implementation is correct for all the examples below that it supports.↓ Show more ↓ Basix.UFL basix.ElementFamily.DPC, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True↓ Show Basix.UFL examples ↓ This implementation is correct for all the examples below that it supports.↓ Show more ↓ FIAT FIAT.DPC↓ Show FIAT examples ↓ This implementation is correct for all the examples below. Symfem "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

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

## DefElement stats

 Element added 01 March 2021 Element last updated 16 September 2023