an encyclopedia of finite element definitions
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Alternative names | TNT |
De Rham complex families | \(\left[S_{3,k}^\square\right]_{0}\) |
Orders | \(1\leqslant k\) |
Reference elements | quadrilateral, 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) ↓ Show polynomial set definitions ↓ |
DOFs | On 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 DOFs | quadrilateral: \((k+1)^2 + 4\) hexahedron: \((k+1)^3 + 12\) |
Mapping | identity |
continuity | Function values are continuous. |
Categories | Scalar-valued elements |
Symfem | "TNT" ↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. |
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) |
Element added | 24 October 2021 |
Element last updated | 16 September 2023 |