An adaptive moving mesh method for forced curve shortening flow
Mackenzie, J. A. and Nolan, M. and Rowlatt, C. F. and Insall, R. H. (2019) An adaptive moving mesh method for forced curve shortening flow. SIAM Journal on Scientific Computing, 41 (2). A1170–A1200. ISSN 1064-8275 (https://doi.org/10.1137/18M1211969)
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Abstract
We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve. Central finite differences are used to discretise in space the governing evolution equation for the position vector and a second-order implicit scheme is used for the temporal integration. Simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second-order accuracy. Furthermore, the new method delivers improved solution accuracy compared to the use of uniform arc-length meshes.
ORCID iDs
Mackenzie, J. A. ORCID: https://orcid.org/0000-0003-4412-7057, Nolan, M. ORCID: https://orcid.org/0000-0003-0748-2236, Rowlatt, C. F. and Insall, R. H.;-
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Item type: Article ID code: 66528 Dates: DateEvent18 April 2019Published3 January 2019AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 10 Jan 2019 14:08 Last modified: 30 Nov 2024 14:10 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/66528