Simplified weak Galerkin finite element methods for biharmonic equations on non-convex polytopal meshes

This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite element partitions, utilizing bubble functions as a critical analytical tool. The simplified WG method is symmetric and positive definite. Optimal-order error estimates are established for WG approximations in both the discrete $ H^2 $ norm and the $ L^2 $ norm.