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arXiv · 2601.00986

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

Chunmei Wang·Shangyou Zhang
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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.

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Chunmei Wang, Shangyou Zhang. 2026-01-02. A Simple Weak Galerkin Finite Element Method for Convection-Diffusion-Reaction Equations on Nonconvex Polytopal Meshes. https://arxiv.org/abs/2601.00986

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