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Arnold–Winther

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Alternative namesconforming Arnold–Winther
Orders\(3\leqslant k\)
Reference elementstriangle
Polynomial set\(\mathcal{Z}^{(27)}_{k-1} \oplus \mathcal{Z}^{(28)}_{k}\)
↓ Show polynomial set definitions ↓
DOFsOn each vertex: point evaluations of three components
On each edge: integral moments of normal-normal and normal-tangent inner products with an order \(k-2\) Lagrange space
On each face: integral moments of three components with an order \(k-3\) Lagrange space, and integral moments of tensor dot product with \(\frac{\partial}{\partial(x, y)}x^2y^2(1-x-y)^2f\) for each order \(k-4\) polynomial \(f\) in an order \(k-4\) Lagrange space
Number of DOFstriangle: \((3k^2+5k+6)/2\)
CategoriesMatrix-valued elements

Implementations

Symfem"AW"
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UFL"AWc"
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Examples

triangle
order 3

(click to view basis functions)
triangle
order 4

(click to view basis functions)

References

DefElement stats

Element added10 February 2021
Element last updated02 August 2022