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DPc

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Alternative namesdiscontinuous polynomial cubical
Exterior calculus names\(\mathcal{S}_{k}\Lambda^{d}(\square_d)\), \(\mathcal{S}^-_{k}\Lambda^{d}(\square_d)\)
Cockburn–fu names\(\left[S_{1,k}^\square\right]_{d}\), \(\left[S_{2,k}^\square\right]_{d}\)
Orders\(0\leqslant k\)
Reference elementsinterval, quadrilateral, hexahedron
Polynomial set\(\mathcal{P}_{k}\)
↓ Show polynomial set definitions ↓
DOFsOn the interior of the reference element: point evaluations
Number of DOFsinterval: \(k+1\) (A000027)
quadrilateral: \((k+1)(k+2)/2\) (A000217)
hexahedron: \((k+1)(k+2)(k+3)/6\) (A000292)
Mappingidentity
continuityDiscontinuous.
CategoriesScalar-valued elements

Implementations

Basixbasix.ElementFamily.DPC (quadrilateral, hexahedron)
↓ Show Basix examples ↓
Symfem"dPc"
↓ Show Symfem examples ↓
UFL"DPC"
↓ Show UFL examples ↓

Examples

interval
order 1

(click to view basis functions)
interval
order 2

(click to view basis functions)
interval
order 3

(click to view basis functions)
quadrilateral
order 1

(click to view basis functions)
quadrilateral
order 2

(click to view basis functions)
quadrilateral
order 3

(click to view basis functions)

References

DefElement stats

Element added01 March 2021
Element last updated02 August 2022