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Lectures on the Error Analysis of Interpolation on Simplicial Triangulations without the Shape Regularity Assumption and Its Applications to Finite Element Methods Part 1: Lagrange Interpolation on Triangles
https://doi.org/10.60217/0002002440
https://doi.org/10.60217/0002002440c72c1166-9914-4021-a6e1-2bba27a50ed6
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
AN10408332_2022_24_02.pdf (252 KB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2024-02-15 | |||||||||||||
| タイトル | ||||||||||||||
| タイトル | Lectures on the Error Analysis of Interpolation on Simplicial Triangulations without the Shape Regularity Assumption and Its Applications to Finite Element Methods Part 1: Lagrange Interpolation on Triangles | |||||||||||||
| 言語 | en | |||||||||||||
| 言語 | ||||||||||||||
| 言語 | eng | |||||||||||||
| キーワード | ||||||||||||||
| 言語 | en | |||||||||||||
| 主題Scheme | Other | |||||||||||||
| 主題 | lagrange interpolation | |||||||||||||
| キーワード | ||||||||||||||
| 言語 | en | |||||||||||||
| 主題Scheme | Other | |||||||||||||
| 主題 | shape-regurality | |||||||||||||
| キーワード | ||||||||||||||
| 言語 | en | |||||||||||||
| 主題Scheme | Other | |||||||||||||
| 主題 | maximum angle | |||||||||||||
| キーワード | ||||||||||||||
| 言語 | en | |||||||||||||
| 主題Scheme | Other | |||||||||||||
| 主題 | finite elements | |||||||||||||
| 資源タイプ | ||||||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||
| 資源タイプ | departmental bulletin paper | |||||||||||||
| ID登録 | ||||||||||||||
| ID登録 | 10.60217/0002002440 | |||||||||||||
| ID登録タイプ | JaLC | |||||||||||||
| アクセス権 | ||||||||||||||
| アクセス権 | open access | |||||||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||||||
| 著者 |
小林, 健太
× 小林, 健太
× 土屋, 卓也
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| 抄録 | ||||||||||||||
| 内容記述タイプ | Abstract | |||||||||||||
| 内容記述 | In the error analysis of finite element methods, the shape regularity assumption on triangulations is typically imposed to obtain a priori error estimations. In practical computations, however, very "thin" or "degenerated" elements that violate the shape regularity assumption may appear when we use adaptive mesh refinement. In this survey, we attempt to establish an error analysis approach without the shape regularity assumption on triangulations. We have presented several papers on the error analysis of finite element methods on non-shape regular triangulations. The main points in these papers are that, in the error estimates of finite element methods, the circumradius of the triangles is one of the most important factors. The purpose of this survey is to provide a simple and plain explanation of the results to researchers and, in particular, graduate students who are interested in the subject. Therefore, this survey is not intended to be a research paper. We hope that, in the near future, it will be merged into a textbook on the mathematical theory of the finite element methods. |
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| 言語 | en | |||||||||||||
| 書誌情報 |
ja : 愛媛大学理学部紀要 en : Memoirs of the Faculty of Science, Ehime University 巻 24, p. 9-42, ページ数 34, 発行日 2022 |
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| 出版者 | ||||||||||||||
| 出版者 | 愛媛大学理学部 | |||||||||||||
| 言語 | ja | |||||||||||||
| ISSN | ||||||||||||||
| 収録物識別子タイプ | EISSN | |||||||||||||
| 収録物識別子 | 09195203 | |||||||||||||
| 書誌レコードID | ||||||||||||||
| 収録物識別子タイプ | NCID | |||||||||||||
| 収録物識別子 | AN10408332 | |||||||||||||
| 著者版フラグ | ||||||||||||||
| 出版タイプ | VoR | |||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||||
