an encyclopedia of finite element definitions
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Degrees | interval: \(k=2\) triangle: \(k=3\) tetrahedron: \(k=4\) |
Polynomial subdegree | interval: \(k + 1\) triangle: \(k\) tetrahedron: \(k\) |
Polynomial superdegree | \(k+1\) |
Lagrange subdegree | interval: \(k + 1\) triangle: \(k\) tetrahedron: \(k\) |
Lagrange superdegree | \(k+1\) |
Reference elements | interval, triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(52)}_{k}\) (interval) \(\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(53)}_{k}\) (triangle) \(\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(54)}_{k}\) (tetrahedron) ↓ Show polynomial set definitions ↓ |
DOFs | On each vertex: point evaluations On each edge: integrals of normal derivatives On each face: integrals of normal derivatives On each volume: integrals of normal derivatives |
Number of DOFs | interval: \(4\) triangle: \(12\) tetrahedron: \(38\) |
Mapping | identity |
continuity | Function values are continuous. |
Categories | Scalar-valued elements |
interval degree 2 | (click to view basis functions) |
triangle degree 3 | (click to view basis functions) |
tetrahedron degree 4 | (click to view basis functions) |
Element added | 08 June 2021 |
Element last updated | 27 September 2024 |