an encyclopedia of finite element definitions

# Enriched vector Galerkin

 Alternative names locking-free enriched Galerkin Abbreviated names LFEG Orders $$1\leqslant k$$ Reference elements 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

 Symfem "LFEG"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations.

## Examples

 triangleorder 1 (click to view basis functions) triangleorder 2 (click to view basis functions) quadrilateralorder 1 (click to view basis functions) quadrilateralorder 2 (click to view basis functions) tetrahedronorder 1 (click to view basis functions) tetrahedronorder 2 (click to view basis functions) hexahedronorder 1 (click to view basis functions) hexahedronorder 2 (click to view basis functions)
• 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 16 September 2023