Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems
文献类型：期刊论文
| 作者 | Xu, X.1 ; Chen, H.1; Hoppe, R. H. W.2,3
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| 刊名 | JOURNAL OF NUMERICAL MATHEMATICS
 |
| 出版日期 | 2010-04-01 |
| 卷号 | 18期号:1页码:59-90 |
| 关键词 | local multilevel methods adaptive finite element methods local smoothing Schwarz theory optimality |
| ISSN号 | 1570-2820 |
| DOI | 10.1515/JNUM.2010.003 |
| 英文摘要 | A local multilevel product algorithm and its additive version are analyzed for linear systems arising from the application of adaptive finite element methods to second order elliptic boundary value problems. The abstract Schwarz theory is applied to verify uniform convergence of local multilevel methods featuring Jacobi and Gauss-Seidel smoothing only on local nodes. By this abstract theory, convergence estimates can be further derived for the hierarchical basis multigrid method and the hierarchical basis preconditioning method on locally refined meshes, where local smoothing is performed only on new nodes. Numerical experiments confirm the optimality of the suggested algorithms. |
| 资助项目 | National Basic Research Program of China[2005CB321701] ; National Natural Science Foundation of China[10731060] ; NSF[DMS-0707602] ; NSF[DMS-0810156] ; NSF[DMS-0811153] ; NSF[DMS-0914788] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000276911700003 |
| 出版者 | WALTER DE GRUYTER & CO |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/9897]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Xu, X. |
| 作者单位 | 1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Univ Houston, Dept Math, Houston, TX 77204 USA 3.Univ Augsburg, Inst Math, D-86159 Augsburg, Germany |
| 推荐引用方式 GB/T 7714 | Xu, X.,Chen, H.,Hoppe, R. H. W.. Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems[J]. JOURNAL OF NUMERICAL MATHEMATICS,2010,18(1):59-90. |
| APA | Xu, X.,Chen, H.,&Hoppe, R. H. W..(2010).Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems.JOURNAL OF NUMERICAL MATHEMATICS,18(1),59-90. |
| MLA | Xu, X.,et al."Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems".JOURNAL OF NUMERICAL MATHEMATICS 18.1(2010):59-90. |
入库方式： OAI收割
来源：数学与系统科学研究院
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