an encyclopedia of finite element definitions

# Enriched Galerkin

 Abbreviated names EG Orders $$1\leqslant k$$ Reference elements interval, triangle, tetrahedron, quadrilateral, hexahedron, prism, pyramid Number of DOFs interval: $$k+2$$ (A000027)triangle: $$(k+1)(k+2)/2 + 1$$tetrahedron: $$(k+1)(k+2)(k+3)/6 + 1$$quadrilateral: $$(k+1)^2 + 1$$hexahedron: $$(k+1)^3 + 1$$prism: $$(k+1)^2(k+2)/2 + 1$$pyramid: $$(k+1)(k+2)(2k+3)/6 + 1$$ Mapping identity continuity Discontinuous. Notes This is a continuous Lagrange element enriched with a discontinuous piecewise constant element. Categories Scalar-valued elements

## Implementations

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

## Examples

 intervalorder 1 (click to view basis functions) intervalorder 2 (click to view basis functions) 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)

## References

• Sun, Shuyu and Liu, Jiangguo. A locally conservative finite element method based on piecewise constant enrichment of the continuous Galerkin method, SIAM Journal on Scientific Computing 31(4), 2528–2548, 2009. [DOI: 10.1137/080722953] [BibTeX]

## DefElement stats

 Element added 05 March 2023 Element last updated 16 September 2023