an encyclopedia of finite element definitions
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Orders | \(1\leqslant k\leqslant {'interval': 1, 'triangle': 2, 'tetrahedron': 3}\) |
Reference elements | interval, triangle, tetrahedron |
Polynomial set | \(\mathcal{P}_{k}\) ↓ 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: \(k+1\) (A000027) triangle: \((k+1)(k+2)/2\) (A000217) tetrahedron: \((k+1)(k+2)(k+3)/6\) (A000292) |
Mapping | identity |
Categories | Scalar-valued elements |
Symfem | "MWX" ↓ Show Symfem examples ↓ |
interval order 1 | ![]() (click to view basis functions) |
triangle order 1 | ![]() (click to view basis functions) |
triangle order 2 | ![]() (click to view basis functions) |
tetrahedron order 1 | ![]() (click to view basis functions) |
tetrahedron order 2 | ![]() (click to view basis functions) |
tetrahedron order 3 | ![]() (click to view basis functions) |
Element added | 08 June 2021 |
Element last updated | 02 August 2022 |