Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction–diffusion equation on the curve

Styles, Vanessa and Van Yperen, James (2021) Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction–diffusion equation on the curve. Numerical Methods for Partial Differential Equations. pp. 1-30. ISSN 0749-159X

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Abstract

We consider a semidiscrete finite element approximation for a system consisting of the evolution of a planar curve evolving by forced curve shortening flow inside a given bounded domain (Formula presented.), such that the curve meets the boundary (Formula presented.) orthogonally, and the forcing is a function of the solution of a reaction–diffusion equation that holds on the evolving curve. We prove optimal order (Formula presented.) error bounds for the resulting approximation and present numerical experiments.

Item Type: Article
Keywords: error analysis, forced curve shortening flow, parametric finite elements, prescribed boundary contact, surface PDE
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 10 Feb 2022 09:46
Last Modified: 10 Feb 2022 09:46
URI: http://sro.sussex.ac.uk/id/eprint/104286

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