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.

翻译：本文提出了一种避免使用传统稳定化子的简化弱伽辽金有限元方法用于求解双调和方程。所提出的弱伽辽金方法支持有限元剖分中的凸与非凸多面体单元，并采用气泡函数作为关键分析工具。该简化弱伽辽金方法具有对称正定性。针对弱伽辽金近似解，在离散$H^2$范数与$L^2$范数下均建立了最优阶误差估计。