The Stabilizer-Free Weak Galerkin Finite Element Method for the Biharmonic Equation Using Polynomials of Reduced Order
Abstract
In this article, we use the stabilizer-free weak Galerkin (SFWG) finite element method on general polytopal meshes to solve the biharmonic equation. By decreasing the degree of the polynomials on the boundary of weak functions and modifying the definition of the weak Laplacian, this paper not only removes the stabilizer in the weak Galerkin (WG) numerical scheme, but also minimizes the number of unknowns in the scheme. The optimal orders of error estimates in the $H^2$ and $L^2$ norms are obtained and the convergence results are verified by some numerical examples.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Differential Equations and Numerical Methods
Numerical methods in engineering
Publication details
- Journal / source
- International Journal of Numerical Analysis and Modeling
- Publisher
- Global Science Press
- Volume
- 23
- Issue
- 4
- Pages
- 480–498
- Publication date
- 29 May 2026
- Language
- EN