Convergent Finite Elements on Arbitrary Meshes, the WG Method (CSIAM Transactions on Applied Mathematics, 2025)
On meshes with the maximum angle condition violated, the standard conforming, nonconforming, and discontinuous Galerkin finite elements do not convergeto the true solution when the mesh size goes to zero. It is shown that one type of weakGalerkin finite element method converges on triangular and tetrahedral meshes violating the maximum angle condition, i.e. on arbitrary meshes. Numerical tests confirmthe theory.
Keywords: Discontinuous finite element; maximum angle condition; Poisson’s equation; triangular grid; tetrahedral grid.