Error estimation for finite element method on meshes that contain thin elements
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917750639689728 |
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| author | Kobayashi, Kenta Tsuchiya, Takuya |
| author_facet | Kobayashi, Kenta Tsuchiya, Takuya |
| contents | In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if "bad" elements elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error estimation for finite element method on meshes that contain thin elements Kobayashi, Kenta Tsuchiya, Takuya Numerical Analysis 65D05, 65N30 In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if "bad" elements elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result. |
| title | Error estimation for finite element method on meshes that contain thin elements |
| topic | Numerical Analysis 65D05, 65N30 |
| url | https://arxiv.org/abs/2402.18860 |