A Simple Weak Galerkin Finite Element Method for Convection-Diffusion-Reaction Equations on Nonconvex Polytopal Meshes

TL;DR

This paper presents a simple weak Galerkin finite element method for convection-diffusion-reaction equations on complex nonconvex meshes, providing rigorous error estimates and validating efficiency through numerical experiments.

Contribution

The paper introduces a flexible weak Galerkin method that supports discontinuous functions on nonconvex polytopal meshes with proven error bounds.

Findings

Numerical experiments confirm theoretical convergence rates.

The method demonstrates high computational efficiency.

Supports general nonconvex polytopal meshes.

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.