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Hellan–Herrmann–Johnson

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Orders\(0\leqslant k\)
Reference elementstriangle
Polynomial set\(\mathcal{Z}^{(27)}_{k}\)
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DOFsOn each edge: integral moments of inner products of normal to edge with an order \(k\) Lagrange space
On each face: point evaluations of tensor products with symmetric matrices whose entries are in (lagrange,k-1)
Number of DOFstriangle: \(3(k+1)(k+2)/2\) (A045943)
Mappingdouble contravariant Piola
continuityInner products with normals to facets are continuous
CategoriesMatrix-valued elements

Implementations

Symfem"HHJ"
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UFL"HHJ"
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Examples

triangle
order 1

(click to view basis functions)
triangle
order 2

(click to view basis functions)

References

DefElement stats

Element added06 February 2021
Element last updated02 August 2022