an encyclopedia of finite element definitions
Enriched vector Galerkin
Click here to read what the information on this page means.
| Alternative names | locking-free enriched Galerkin |
| Abbreviated names | LFEG |
| Degrees | \(1\leqslant k\) where \(k\) is the polynomial subdegree |
| Polynomial subdegree | \(k\) |
| Polynomial superdegree | triangle: \(k\) tetrahedron: \(k\) quadrilateral: \(dk\) hexahedron: \(dk\) |
| Lagrange subdegree | \(k\) |
| Lagrange superdegree | \(k\) |
| Reference cells | triangle, tetrahedron, quadrilateral, hexahedron |
| Number of DOFs | triangle: \((k+1)(k+2) + 1\) tetrahedron: \((k+1)(k+2)(k+3)/2 + 1\) quadrilateral: \(2(k+1)^2 + 1\) hexahedron: \(3(k+1)^3 + 1\) |
| continuity | Discontinuous. |
| Notes | This is a continuous vector Lagrange element enriched with a single discontinuous function. |
| Categories | Vector-valued elements |
Implementations
This element is implemented in Symfem .↓ Show implementation detail ↓Examples
| triangle degree 1 |  (click to view basis functions) |
| triangle degree 2 |  (click to view basis functions) |
| quadrilateral degree 1 |  (click to view basis functions) |
| quadrilateral degree 2 |  (click to view basis functions) |
| tetrahedron degree 1 |  (click to view basis functions) |
| tetrahedron degree 2 |  (click to view basis functions) |
| hexahedron degree 1 |  (click to view basis functions) |
| hexahedron degree 2 |  (click to view basis functions) |
References
- Yi, Son-Young, Hu, Xiaozhe, Lee, Sanghyun, and Adler, James H. An enriched Galerkin method for the Stokes equations, Computers & Mathematics with Applications 120, 115–131, 2022. [DOI: 10.1016/j.camwa.2022.06.018] [BibTeX]
DefElement stats
| Element added | 07 March 2023 |
| Element last updated | 04 June 2025 |