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

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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.

Keywords

weak Galerkin / weak second order partial derivative / stabilizer-free / bubble functions / non-convex, polytopal meshes / biharmonic equations

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