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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