an encyclopedia of finite element definitions
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Abbreviated names | ABF |
Orders | \(0\leqslant k\) |
Reference elements | quadrilateral |
Polynomial set | \(\mathcal{Z}^{(0)}_{k} \oplus \mathcal{Z}^{(1)}_{k}\) ↓ Show polynomial set definitions ↓ |
DOFs | On each edge: normal integral moments with an order \(k\) Lagrange space On each face: integral moments with an order \(k\) Nédélec (first kind) space, integral moments of the divergence with \(x^{k+1}y^q\) for q=0,1,...,k, and integral moments of the divergence with \(x^qy^{k+1}\) for q=0,1,...,k |
Mapping | contravariant Piola |
continuity | Components normal to facets are continuous |
Categories | Vector-valued elements, H(div) conforming elements |
Symfem | "ABF" ↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. |
quadrilateral order 0 | ![]() (click to view basis functions) |
quadrilateral order 1 | ![]() (click to view basis functions) |
quadrilateral order 2 | ![]() (click to view basis functions) |
Element added | 01 December 2021 |
Element last updated | 16 September 2023 |