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On motion by curvature of a network with a triple junction
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Pozzi, Paola and Stinner, Björn (2021) On motion by curvature of a network with a triple junction. SMAI Journal of Computational Mathematics, 7 . pp. 27-55. doi:10.5802/smai-jcm.70 ISSN 2426-8399.
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WRAP-On-motion-curvature-network-triple-junction-2021.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (2268Kb) | Preview |
Official URL: http://dx.doi.org/10.5802/smai-jcm.70
Abstract
We numerically study the planar evolution by curvature flow of three parametrised curves that are connected by a triple junction in which conditions are imposed on the angles at which the curves meet. One of the key problems in analysing motion of networks by curvature law is the choice of a tangential velocity that allows for motion of the triple junction, does not lead to mesh degeneration, and is amenable to an error analysis. Our approach consists in considering a perturbation of a classical smooth formulation. The problem we propose admits a natural variational formulation that can be discretized with finite elements. The perturbation can be made arbitrarily small when a regularisation parameter shrinks to zero. Convergence of the new semi-discrete finite element scheme including optimal error estimates are proved. These results are supported by some numerical tests. Finally, the influence of the small regularisation parameter on the properties of scheme and the accuracy of the results is numerically investigated.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Curvature -- Mathematics, Differential equations, Nonlinear, Differential equations, Partial, Computer algorithms, Numerical analysis, Mathematics -- Data processing | ||||||
| Journal or Publication Title: | SMAI Journal of Computational Mathematics | ||||||
| Publisher: | Society de Mathematiques Appliques et Industrielles | ||||||
| ISSN: | 2426-8399 | ||||||
| Official Date: | 11 March 2021 | ||||||
| Dates: |
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| Volume: | 7 | ||||||
| Page Range: | pp. 27-55 | ||||||
| DOI: | 10.5802/smai-jcm.70 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Copyright Holders: | © Société de Mathématiques Appliquées et Industrielles, 2021 Certains droits réservés | ||||||
| Date of first compliant deposit: | 19 May 2021 | ||||||
| Date of first compliant Open Access: | 20 May 2021 |
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