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Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Chinese Academy of Sciences, China.
2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 343, 324-339 p.Article in journal (Refereed) Published
Abstract [en]

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 C1 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 H1 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.

Place, publisher, year, edition, pages
Academic Press, 2017. Vol. 343, 324-339 p.
Keyword [en]
Error estimates, Extended loop subdivision, Isogeometric analysis, Minimal surfaces
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-209506DOI: 10.1016/j.jcp.2017.04.030ISI: 000402478300017Scopus ID: 2-s2.0-85018737037OAI: oai:DiVA.org:kth-209506DiVA: diva2:1112960
Funder
Swedish Foundation for Strategic Research , AM13-0049
Note

QC 20170621

Available from: 2017-06-21 Created: 2017-06-21 Last updated: 2017-07-04Bibliographically approved

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CiteExportLink to record
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  • apa
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