Numerical solutions for Biharmonic interface problems via weak Galerkin finite element methods

Abstract

This paper focuses on the advancement of weak Galerkin (WG) finite element methods for addressing two-dimensional and three-dimensional Biharmonic interface problems with polygonal/polyhedral meshes. The WG method has been demonstrated to be accurate and efficient, providing optimal order error estimates in discrete H2 and standard L2 norms. A series of extensive numerical tests are conducted to validate the WG solutions, showcasing the flexibility, stability, and robustness of the proposed method for handling both smooth and complicated interfaces.