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Volume 18, Issue 1
Convergence Analysis of a Weak Galerkin Finite Element Method on a Bakhvalov-Type Mesh for a Singularly Perturbed Convection-Diffusion Equation in 2D

Shicheng Liu, Xiangyun Meng & Qilong Zhai

DOI: 10.4208/aamm.OA-2024-0150

Adv. Appl. Math. Mech., 18 (2026), pp. 348-368.

Published online: 2025-10

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  • Abstract

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.

  • Keywords

Weak Galerkin finite element method, convection-diffusion, singularly perturbed, Bakhvalov-type mesh.

  • AMS Subject Headings

65N15, 65N30, 35B25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-18-348, author = {Liu , ShichengMeng , Xiangyun and Zhai , Qilong}, title = {Convergence Analysis of a Weak Galerkin Finite Element Method on a Bakhvalov-Type Mesh for a Singularly Perturbed Convection-Diffusion Equation in 2D}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {18}, number = {1}, pages = {348--368}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2024-0150}, url = {http://global-sci.org/intro/article_detail/aamm/24530.html} }
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 -

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.

Liu , ShichengMeng , Xiangyun and Zhai , Qilong. (2025). Convergence Analysis of a Weak Galerkin Finite Element Method on a Bakhvalov-Type Mesh for a Singularly Perturbed Convection-Diffusion Equation in 2D. Advances in Applied Mathematics and Mechanics. 18 (1). 348-368. doi:10.4208/aamm.OA-2024-0150
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