Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision

doi:10.1016/j.jcp.2017.04.030

	Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision
	Pan, Qing 1; Chen, Chong2,3 ; Xu, Guoliang 2
	2017-08-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	343 页码:324-339
摘要	In 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.
关键词	Extended loop subdivision Isogeometric analysis Error estimates Minimal surfaces
DOI	10.1016/j.jcp.2017.04.030
语种	英语
资助项目	National 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研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000402478300017
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25543
专题	计算数学与科学工程计算研究所
通讯作者	Pan, Qing
作者单位	1.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
推荐引用方式 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.