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

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 Ω⊂ℝ2, such that the curve meets the boundary ∂Ω orthogonally, and the forcing is a function of the solution of a r...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2023-01, Vol.39 (1), p.133-162
Main Authors: Styles, Vanessa, Van Yperen, James
Format: Article
Language:English
Subjects:
Approximation
Diffusion
error analysis
Evolution
forced curve shortening flow
Mathematical analysis
Numerical analysis
parametric finite elements
prescribed boundary contact
Reaction-diffusion equations
surface PDE
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Summary: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 Ω⊂ℝ2, such that the curve meets the boundary ∂Ω 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 H1 error bounds for the resulting approximation and present numerical experiments.
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22861