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Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision
Pan, Qing1; Chen, Chong2,3; Xu, Guoliang2
2017-08-15
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume343Pages:324-339
AbstractIn this paper, we investigate the formulation of isogeometric analysis for minimal surface models on planar bounded domains by extended Loop surface subdivision approach. The exactness of the physical domain of interest is fixed on the coarsest level of the triangular discretization with any topological structure, which is thought of as the initial control mesh of Loop subdivision. By performing extended Loop subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of quartic box-spline while maintaining its original exactness. The limit function representation of extended Loop subdivision forms our finite element space, which possesses C-1 smoothness and the flexibility of mesh topology. We establish its inverse inequalities which resemble the ones of general finite element spaces. We develop the approximation estimate with the aid of H-1 convergence property of the corresponding linear models. It enables us to overcome the difficulty of proving the boundedness of the gradient of finite element solutions appearing in the coefficient of minimal surface models. Numerical examples are given with the comparison to the classical linear finite element method which is consistent with our theoretical results. (C) 2017 Elsevier Inc. All rights reserved.
KeywordExtended loop subdivision Isogeometric analysis Error estimates Minimal surfaces
DOI10.1016/j.jcp.2017.04.030
Language英语
Funding ProjectNational Natural Science Foundation of China (NSFC)[11671130] ; Scientific Research Fund of Hunan Provincial Education Department[15A110] ; NSFC[11301520] ; Swedish Foundation for Strategic Research grant[AM13-0049] ; NSFC Funds for Creative Research Groups of China[11321061]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000402478300017
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25543
Collection计算数学与科学工程计算研究所
Affiliation1.Hunan Normal Univ, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
3.Royal Inst Technol KTH, Dept Math, S-10044 Stockholm, Sweden
Recommended Citation
GB/T 7714
Pan, Qing,Chen, Chong,Xu, Guoliang. Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,343:324-339.
APA Pan, Qing,Chen, Chong,&Xu, Guoliang.(2017).Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision.JOURNAL OF COMPUTATIONAL PHYSICS,343,324-339.
MLA Pan, Qing,et al."Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision".JOURNAL OF COMPUTATIONAL PHYSICS 343(2017):324-339.
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