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Local Multigrid in H(curl)
Hiptmair, Ralf1; Zheng, Weiying2
2009-09-01
发表期刊JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
卷号27期号:5页码:573-603
摘要We consider H(curl, Omega)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H(1)(Omega)-context along with local discrete Helmholtz-type decompositions of the edge element space.
关键词Edge elements Local multigrid Stable multilevel splittings Subspace correction theory Regular decompositions of H(curl, Omega) Helmholtz-type decompositions Local mesh refinement
DOI10.4208/jcm.2009.27.5.012
语种英语
WOS研究方向Mathematics
WOS类目Mathematics, Applied ; Mathematics
WOS记录号WOS:000267903700003
出版者VSP BV
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/9069
专题计算数学与科学工程计算研究所
通讯作者Hiptmair, Ralf
作者单位1.Swiss Fed Inst Technol, SAM, CH-8092 Zurich, Switzerland
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
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Hiptmair, Ralf,Zheng, Weiying. Local Multigrid in H(curl)[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2009,27(5):573-603.
APA Hiptmair, Ralf,&Zheng, Weiying.(2009).Local Multigrid in H(curl).JOURNAL OF COMPUTATIONAL MATHEMATICS,27(5),573-603.
MLA Hiptmair, Ralf,et al."Local Multigrid in H(curl)".JOURNAL OF COMPUTATIONAL MATHEMATICS 27.5(2009):573-603.
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