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LOCAL MULTILEVEL METHODS WITH RECTANGULAR FINITE ELEMENTS FOR THE BIHARMONIC PROBLEM
Tang, Shibing1; Xu, Xuejun1,2
2017
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume39Issue:6Pages:A2592-A2615
AbstractIn this paper, some local multilevel methods are presented to solve the linear algebraic systems resulting from the application of adaptive conforming Bogner-Fox-Schmit rectangular element and nonconforming Adini rectangular element approximations to the biharmonic problem. The abstract Schwarz framework is applied to verify the uniform convergence of the local multilevel methods featuring Jacobi and Gauss-Seidel smoothing only on local nodes associated with the local refinements. By the abstract framework, a convergence estimate may also be derived from the stability of the space splitting and its strengthened Cauchy Schwarz inequality. We demonstrate the optimality of the proposed algorithms by extensive numerical experiments.
Keywordbiharmonic problem Schwarz framework Bogner-Fox-Schmit element Adini element local multilevel method
DOI10.1137/17M111008X
Language英语
Funding ProjectNational Natural Science Foundation of China[11671302]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418659900019
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27013
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
2.Tongji Univ, Sch Math Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Tang, Shibing,Xu, Xuejun. LOCAL MULTILEVEL METHODS WITH RECTANGULAR FINITE ELEMENTS FOR THE BIHARMONIC PROBLEM[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2017,39(6):A2592-A2615.
APA Tang, Shibing,&Xu, Xuejun.(2017).LOCAL MULTILEVEL METHODS WITH RECTANGULAR FINITE ELEMENTS FOR THE BIHARMONIC PROBLEM.SIAM JOURNAL ON SCIENTIFIC COMPUTING,39(6),A2592-A2615.
MLA Tang, Shibing,et al."LOCAL MULTILEVEL METHODS WITH RECTANGULAR FINITE ELEMENTS FOR THE BIHARMONIC PROBLEM".SIAM JOURNAL ON SCIENTIFIC COMPUTING 39.6(2017):A2592-A2615.
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