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Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve

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Title: Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve
Authors: Barrett, JW
Deckelnick, K
Styles, V
Item Type: Journal Article
Abstract: We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution is based on a parametric description allowing for tangential motion, whereas the discretisation for the PDE on the curve uses an idea from [6]. We prove optimal error bounds for the resulting fully discrete approximation and present numerical experiments. These confirm our estimates and also illustrate the advantage of the tangential motion of the mesh points in practice.
Issue Date: 25-Apr-2017
Date of Acceptance: 15-Feb-2017
URI: http://hdl.handle.net/10044/1/44721
DOI: https://dx.doi.org/10.1137/16M1083682
ISSN: 0036-1429
Publisher: Society for Industrial and Applied Mathematics
Start Page: 1080
End Page: 1100
Journal / Book Title: SIAM Journal on Numerical Analysis
Volume: 55
Issue: 2
Copyright Statement: © 2017, Society for Industrial and Applied Mathematics
Keywords: Numerical & Computational Mathematics
0103 Numerical And Computational Mathematics
Publication Status: Published
Article Number: 55
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences