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Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve
Version 2 2023-06-12, 08:39
Version 1 2023-06-09, 05:24
journal contribution
posted on 2023-06-12, 08:39 authored by John W Barrett, Klaus Deckelnick, Vanessa StylesVanessa StylesWe 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.
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- Published
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- Published version
Journal
SIAM Journal on Numerical Analysis (SINUM)ISSN
0036-1429Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
2Volume
55Page range
1080-1100Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
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- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-03-08First Open Access (FOA) Date
2017-03-08First Compliant Deposit (FCD) Date
2017-03-08Usage metrics
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