Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes
Abstract
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 H2 norm and the L2 norm.
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