A modified weak Galerkin finite element method for parabolic equations on anisotropic meshes

In this paper, we study a modified weak Galerkin finite element method (MWG-FEM) on anisotropic triangular meshes for a class of parabolic equations. Different from conventional weak Galerkin methods, the MWG-FEM replaces the boundary functions by the average of interior functions, which possesses flexibility in the approximation functions and mesh generation. Moreover, MWG-FEM is compatible with anisotropic meshes and suitable for solving problems with anisotropic property. By using the anisotropic interpolation and projection operators, the optimal order error estimate in L2 norm is derived. Numerical experiments are performed to demonstrate the stability and efficiency of the method. & COPY; 2023 Elsevier Ltd. All rights reserved.