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

Barrett, John W, Deckelnick, Klaus and Styles, Vanessa (2017) Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve. SIAM Journal on Numerical Analysis (SINUM), 55 (2). pp. 1080-1100. ISSN 0036-1429

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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 discretization for the PDE on the curve uses an idea from [G. Dziuk and C. M. Elliott, IMA J. Numer. Anal., 27 (2007), pp. 262--292]. 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Vanessa Styles
Date Deposited: 08 Mar 2017 14:51
Last Modified: 23 Aug 2017 04:44
URI: http://sro.sussex.ac.uk/id/eprint/67029

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