Computational aspects of hyperbolic curvature flow

Monika Suchomelová, Michal Beneš and Miroslav Kolář

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: The article analyzes behavior of the solution of the hyperbolic curvature flow by means of a class of analytical solutions and by computational studies performed by a semi-discrete finite-volume scheme. A class of analytical solutions is derived and used for the verification of the computational algorithm by numerical convergence to it. An original tangential redistribution is proposed to stabilize the numerical scheme. Its derivation requires a four-dimensional transformation of the evolution law. The role of tangential redistribution is demonstrated on computational examples. Computational studies show evolution of the initially convex and non-convex curves, and include cases when singularities predicted by theory start to develop.

Keywords: Curvature driven flow; Parametric curve description; Hyperbolic curvature flow; Flowing finite-volume method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000281

DOI: 10.1016/j.amc.2025.129301

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