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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
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Official URL: https://doi.org/10.1093/imanum/dry004
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 > 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: |
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| Date of first compliant deposit: | 10 January 2018 | ||||||||
| Date of first compliant Open Access: | 6 March 2019 | ||||||||
| 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 | ||||||||
| Open Access Version: |
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