TY - JOUR
T1 - Convergence Analysis of a Weak Galerkin Finite Element Method on a Bakhvalov-Type Mesh for a Singularly Perturbed Convection-Diffusion Equation in 2D
AU - Liu , Shicheng
AU - Meng , Xiangyun
AU - Zhai , Qilong
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 348
EP - 368
PY - 2025
DA - 2025/10
SN - 18
DO - http://doi.org/10.4208/aamm.OA-2024-0150
UR - https://global-sci.org/intro/article_detail/aamm/24530.html
KW - Weak Galerkin finite element method, convection-diffusion, singularly perturbed, Bakhvalov-type mesh.
AB - <p style="text-align: justify;">In this paper, we propose a weak Galerkin finite element method (WG) for solving singularly perturbed convection-diffusion problems on a Bakhvalov-type mesh in 2D. Our method is flexible and allows the use of discontinuous approximation functions on the mesh. An error estimate is developed in a suitable norm, and the optimal convergence order is obtained. Finally, numerical experiments are conducted to support the theory and to demonstrate the efficiency of the proposed method.</p>