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Vector Q

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Alternative namesvector Lagrange
Orders\(0\leqslant k\)
Reference elementsquadrilateral, hexahedron
Polynomial set\(\mathcal{Q}_{k}^d\)
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DOFsOn 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 DOFsinterval: \(k+1\) (A000027)
quadrilateral: \(2(k+1)^2\) (A001105)
hexahedron: \(3(k+1)^3\) (A117642)
Mappingidentity
continuityFunction values are continuous.
CategoriesVector-valued elements

Implementations

Symfem"vector Q"
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UFL"Q"
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Examples

quadrilateral
order 1
(click to view basis functions)
quadrilateral
order 2
(click to view basis functions)
hexahedron
order 1
(click to view basis functions)
hexahedron
order 2
(click to view basis functions)

DefElement stats

Element added30 December 2020
Element last updated02 August 2022