@article{Wang2025, 
author = {Chunmei Wang},
title = {Simplified weak Galerkin finite element methods for biharmonic equations on non-convex polytopal meshes},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {3},
pages = {1523-1540},
keywords = {weak Galerkin, weak second order partial derivative, stabilizer-free, bubble functions, non-convex, polytopal meshes, biharmonic equations},
url = {https://www.sciopen.com/article/10.3934/era.2025072},
doi = {10.3934/era.2025072},
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        H    2   norm and the        L    2   norm.}
}