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.

翻译：当网格违反最大角条件时，标准协调元、非协调元及间断Galerkin有限元在网格尺寸趋于零时无法收敛至真解。研究表明，一类弱Galerkin有限元方法能在违反最大角条件（即任意网格）的三角形及四面体网格上保持收敛。数值实验验证了该理论。