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Tiniest tensor

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Alternative namesTNT
Cockburn–fu names\(\left[S_{3,k}^\square\right]_{0}\)
Orders\(1\leqslant k\)
Reference elementsquadrilateral, hexahedron
Polynomial set\(\mathcal{Q}_{k} \oplus \mathcal{Z}^{(31)}_{k}\) (quadrilateral)
\(\mathcal{Q}_{k} \oplus \mathcal{Z}^{(32)}_{k} \oplus \mathcal{Z}^{(33)}_{k} \oplus \mathcal{Z}^{(34)}_{k}\) (hexahedron)
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DOFsOn each vertex: point evaluations
On each edge: integral moments with \(\frac{\partial}{\partial x}f\) for each \(f\) in an order \(k\) Lagrange space
On each face: integral moments with \(\Delta f\) for each \(f\) in an order \(k\) Lagrange space such that the trace of \(f\) on the edges of the face is 0
On each volume: integral moments of gradient with \(\nabla f\) for each \(f\) in an order \(k\) Lagrange space such that the trace of \(f\) on the faces of the volume is 0
Number of DOFsquadrilateral: \((k+1)^2 + 4\)
hexahedron: \((k+1)^3 + 12\)
Mappingidentity
continuityFunction values are continuous.
CategoriesScalar-valued elements

Implementations

Symfem"TNT" (quadrilateral, hexahedron)
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Examples

quadrilateral
order 1

(click to view basis functions)
quadrilateral
order 2

(click to view basis functions)
quadrilateral
order 3

(click to view basis functions)
hexahedron
order 1

(click to view basis functions)

References

DefElement stats

Element added24 October 2021
Element last updated02 August 2022