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Orders | \(k=3\) |
Reference elements | interval, triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k}\) ↓ Show polynomial set definitions ↓ |
DOFs | On each vertex: point evaluations, and point evaluations of derivatives in coordinate directions On each face: point evaluations at midpoints |
Number of DOFs | interval: \(4\) triangle: \(10\) tetrahedron: \(20\) |
Mapping | identity |
continuity | Function values are continuous. |
Notes | The derivatives of the basis functions are continuous between cells at the vertices of the element |
Categories | Scalar-valued elements |
Basix | basix.ElementFamily.Hermite ↓ Show Basix examples ↓ |
Symfem | "Hermite" ↓ Show Symfem examples ↓ |
UFL | "Hermite" ↓ Show UFL examples ↓ |
interval order 3 | ![]() (click to view basis functions) |
triangle order 3 | ![]() (click to view basis functions) |
tetrahedron order 3 | ![]() (click to view basis functions) |
Element added | 09 January 2021 |
Element last updated | 18 May 2023 |