an encyclopedia of finite element definitions
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Alternative names | conforming Arnold–Winther |
Orders | \(3\leqslant k\) |
Reference elements | triangle |
Polynomial set | \(\mathcal{Z}^{(2)}_{k-1} \oplus \mathcal{Z}^{(3)}_{k}\) ↓ Show polynomial set definitions ↓ |
DOFs | On 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 DOFs | triangle: \((3k^2+5k+6)/2\) |
Categories | Matrix-valued elements |
Symfem | "AW" ↓ Show Symfem examples ↓ |
UFL | "AWc" ↓ Show UFL examples ↓ |
triangle order 3 | ![]() (click to view basis functions) |
triangle order 4 | ![]() (click to view basis functions) |
Element added | 10 February 2021 |
Element last updated | 02 August 2022 |