Convergent finite elements on arbitrary meshes, the WG method
Numerical Analysis
2024-07-30 v1 Numerical Analysis
Abstract
On meshes with the maximum angle condition violated, the standard conforming, nonconforming, and discontinuous Galerkin finite elements do not converge to the true solution when the mesh size goes to zero. It is shown that one type of weak Galerkin finite element method converges on triangular and tetrahedral meshes violating the maximum angle condition, i.e., on arbitrary meshes. Numerical tests confirm the theory.
Cite
@article{arxiv.2407.19382,
title = {Convergent finite elements on arbitrary meshes, the WG method},
author = {Ran Zhang and Shangyou Zhang},
journal= {arXiv preprint arXiv:2407.19382},
year = {2024}
}