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

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Version 2 2023-06-12, 08:39
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journal contribution
posted on 2023-06-12, 08:39 authored by John W Barrett, Klaus Deckelnick, Vanessa StylesVanessa Styles
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.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Numerical Analysis (SINUM)

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

2

Volume

55

Page range

1080-1100

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-03-08

First Open Access (FOA) Date

2017-03-08

First Compliant Deposit (FCD) Date

2017-03-08

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