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Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects

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Title: Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects
Authors: Nurnberg, R
Barrett, JW
Garcke, H
Item Type: Journal Article
Abstract: © 2016 Society for Industrial and Applied Mathematics.A new stable continuous-in-time semidiscrete parametric finite element method for Willmore flow is introduced. The approach allows for spontaneous curvature and area difference elasticity effects, which are important for many applications, in particular, in the context of membranes. The method extends ideas from Dziuk and the present authors to obtain an approximation that allows for a tangential redistribution of mesh points, which typically leads to better mesh properties. Moreover, we consider volume and surface area preserving variants of these schemes and, in particular, we obtain stable approximations of Helfrich flow. We also discuss fully discrete variants and present several numerical computations.
Issue Date: 7-Jun-2016
Date of Acceptance: 16-Mar-2016
URI: http://hdl.handle.net/10044/1/30421
DOI: http://dx.doi.org/10.1137/16M1065379
ISSN: 0036-1429
Publisher: Society for Industrial and Applied Mathematics
Start Page: 1732
End Page: 1762
Journal / Book Title: SIAM Journal on Numerical Analysis
Volume: 54
Issue: 3
Copyright Statement: © 2016 Society for Industrial and Applied Mathematics
Keywords: Numerical & Computational Mathematics
0103 Numerical And Computational Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences