Generalized weak Galerkin finite element methods for biharmonic equations

• Published in: Journal of computational and applied mathematics Vol. 434; p. 115353
• Main Authors: Li, Dan, Wang, Chunmei, Wang, Junping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.12.2023
• Subjects: Biharmonic equation; Finite element methods; Generalized discrete weak second order partial derivative; Generalized weak Galerkin; Polytopal partitions; secondary; Generalized weak Galerkin; Polytopal partitions; Biharmonic equation; Finite element methods; Generalized discrete weak second order partial derivative; primary
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2023.115353

The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is introduced in the gWG scheme to allow arbitrary combinations of piecewise polynomial functions defined in the interior and on the boundary of general polygonal or polyhedral elements. The error estimates are established for the numerical approximation in a discrete H2 norm and a L2 norm. The numerical results are reported to demonstrate the accuracy and flexibility of our proposed gWG method for the biharmonic equation.