Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911885731823616 |
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| author | Liu, Shicheng Meng, Xiangyun Zhai, Qilong |
| author_facet | Liu, Shicheng Meng, Xiangyun Zhai, Qilong |
| contents | 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 meshe. An error estimate is devised in a suitable norm and the optimal convergence order is obtained. Finally, numerical experiments are given to support the theory and to show the efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15136 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D Liu, Shicheng Meng, Xiangyun Zhai, Qilong Numerical Analysis 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 meshe. An error estimate is devised in a suitable norm and the optimal convergence order is obtained. Finally, numerical experiments are given to support the theory and to show the efficiency of the proposed method. |
| title | Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.15136 |