A Simple Weak Galerkin Finite Element Method for Convection-Diffusion-Reaction Equations on Nonconvex Polytopal Meshes
Numerical Analysis
2026-01-06 v1 Numerical Analysis
Abstract
This article introduces a simple weak Galerkin (WG) finite element method for solving convection-diffusion-reaction equation. The proposed method offers significant flexibility by supporting discontinuous approximating functions on general nonconvex polytopal meshes. We establish rigorous error estimates within a suitable norm. Finally, numerical experiments are presented to validate the theoretical convergence rates and demonstrate the computational efficiency of the approach.
Keywords
Cite
@article{arxiv.2601.00986,
title = {A Simple Weak Galerkin Finite Element Method for Convection-Diffusion-Reaction Equations on Nonconvex Polytopal Meshes},
author = {Chunmei Wang and Shangyou Zhang},
journal= {arXiv preprint arXiv:2601.00986},
year = {2026}
}
Comments
24 pages, 16 tables, 4 figures