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DPc

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Alternative namesdiscontinuous polynomial cubical
De Rham complex families\(\left[S_{1,k}^\square\right]_{d}\) or \(\mathcal{S}_{k}\Lambda^{d}(\square_d)\), \(\left[S_{2,k}^\square\right]_{d}\) or \(\mathcal{S}^-_{k}\Lambda^{d}(\square_d)\)
Degrees\(0\leqslant k\)
where \(k\) is the Lagrange superdegree
Polynomial subdegree\(k\)
Polynomial superdegree\(k\)
Lagrange subdegree\(\operatorname{floor}(k/d)\)
Lagrange superdegree\(k\)
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

This element is implemented in Basix , Basix.UFL , FIAT , Symfem , and (legacy) UFL.↓ Show implementation detail ↓

Examples

interval
degree 1

(click to view basis functions)
interval
degree 2

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interval
degree 3

(click to view basis functions)
quadrilateral
degree 1

(click to view basis functions)
quadrilateral
degree 2

(click to view basis functions)
quadrilateral
degree 3

(click to view basis functions)

References

DefElement stats

Element added01 March 2021
Element last updated27 September 2024