Convergent finite elements on arbitrary meshes, the WG method - ArXiv:2407.19382

Title: Convergent finite elements on arbitrary meshes, the WG method

Authors: Ran Zhang, Shangyou Zhang

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.