Article
| Title: | Error estimation for finite element solutions on meshes that contain thin elements (English) |
| Author: | Kobayashi, Kenta |
| Author: | Tsuchiya, Takuya |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 69 |
| Issue: | 5 |
| Year: | 2024 |
| Pages: | 571-588 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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 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. (English) |
| Keyword: | finite element method |
| Keyword: | triangulation |
| Keyword: | minimum and maximum angle condition |
| Keyword: | shape regularity condition |
| Keyword: | bad triangles |
| MSC: | 65D05 |
| MSC: | 65N30 |
| DOI: | 10.21136/AM.2024.0047-24 |
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| Date available: | 2024-11-01T12:52:08Z |
| Last updated: | 2024-11-05 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152631 |
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