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Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision
Pan, Qing1; Chen, Chong2,3; Xu, Guoliang2
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
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
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Document Type期刊论文
Corresponding AuthorPan, Qing
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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