Convergence analysis of the adaptive finite element method with the red-green refinement
文献类型：期刊论文
| 作者 | Zhao XuYing3,4 ; Hu Jun1,2; Shi ZhongCi3
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2010-02-01 |
| 卷号 | 53期号:2页码:499-512 |
| 关键词 | red-green refinement adaptive finite element method convergence non-nested local refinement |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-009-0200-x |
| 英文摘要 | In this paper, we analyze the convergence of the adaptive conforming P(1) element method with the red-green refinement. Since the mesh after re. ning is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B). |
| 资助项目 | Natural Science Foundation of China[10601003] ; Natural Science Foundation of China[10971005] ; Foundation for the Author of National Excellent Doctoral Dissertation of China[200718] ; National Basic Research Program of China[2005CB321704] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000276596100022 |
| 出版者 | SCIENCE CHINA PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/10114]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Hu Jun |
| 作者单位 | 1.Peking Univ, Key Lab Math & Appl Math, Minist Educ, Beijing 100871, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhao XuYing,Hu Jun,Shi ZhongCi. Convergence analysis of the adaptive finite element method with the red-green refinement[J]. SCIENCE CHINA-MATHEMATICS,2010,53(2):499-512. |
| APA | Zhao XuYing,Hu Jun,&Shi ZhongCi.(2010).Convergence analysis of the adaptive finite element method with the red-green refinement.SCIENCE CHINA-MATHEMATICS,53(2),499-512. |
| MLA | Zhao XuYing,et al."Convergence analysis of the adaptive finite element method with the red-green refinement".SCIENCE CHINA-MATHEMATICS 53.2(2010):499-512. |
入库方式： OAI收割
来源：数学与系统科学研究院
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