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Elastic flow interacting with a lateral diffusion process : the one-dimensional graph case

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Pozzi, Paola and Stinner, Björn (2019) Elastic flow interacting with a lateral diffusion process : the one-dimensional graph case. IMA Journal of Numerical Analysis, 39 (1). pp. 201-234. doi:10.1093/imanum/dry004 ISSN 1464-3642.

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Official URL: https://doi.org/10.1093/imanum/dry004

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Abstract

A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which is enabled thanks to second-order operator splitting. The error analysis builds up on previous results for the elastic flow. To obtain an error estimate for the quantity on the curve a better control of the velocity is required. For this purpose, a penalty approach is employed and then combined with a generalized Gronwall lemma. Numerical simulations support the theoretical convergence results. Further numerical experiments indicate stability beyond the parameter regime with respect to the penalty term that is covered by the theory.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Geometric analysis, Finite element method, Convergence
Journal or Publication Title: IMA Journal of Numerical Analysis
Publisher: Oxford University Press
ISSN: 1464-3642
Official Date: 25 January 2019
Dates:
DateEvent
25 January 2019Published
6 March 2018Available
8 January 2018Accepted
Volume: 39
Number: 1
Page Range: pp. 201-234
DOI: 10.1093/imanum/dry004
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 10 January 2018
Date of first compliant Open Access: 6 March 2019
Open Access Version:
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