Supercloseness of the HDG method on Shishkin mesh for a singularly perturbed convection diffusion problem in 2D
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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_ | 1866909232423501824 |
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| author | Ma, Xiaoqi Zhang, Jin |
| author_facet | Ma, Xiaoqi Zhang, Jin |
| contents | This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary difficulty lies in accurately estimating the convection term in the layer, where existing methods often fall short. To address this, a novel error control technique is employed, along with reasonable assumptions regarding the stabilization function. The results show that, with polynomial degrees not exceeding $k$, the method achieves supercloseness of almost $k+\frac{1}{2}$ order in an energy norm. Numerical experiments confirm the theoretical accuracy and efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supercloseness of the HDG method on Shishkin mesh for a singularly perturbed convection diffusion problem in 2D Ma, Xiaoqi Zhang, Jin Numerical Analysis This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary difficulty lies in accurately estimating the convection term in the layer, where existing methods often fall short. To address this, a novel error control technique is employed, along with reasonable assumptions regarding the stabilization function. The results show that, with polynomial degrees not exceeding $k$, the method achieves supercloseness of almost $k+\frac{1}{2}$ order in an energy norm. Numerical experiments confirm the theoretical accuracy and efficiency of the proposed method. |
| title | Supercloseness of the HDG method on Shishkin mesh for a singularly perturbed convection diffusion problem in 2D |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.18948 |