An unconditionally stable finite element scheme for anisotropic curve shortening flow

Deckelnick, Klaus ; Nürnberg, Robert

Archivum mathematicum, Tome 59 (2023) no. 3, pp. 263-274

Abstract (VO)

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.

Détail

DOI : 10.5817/AM2023-3-263

Classification : 35K15, 53E10, 65M12, 65M60
Keywords: anisotropic curve shortening flow; finite element method; stability

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