Address:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany
Dipartimento di Mathematica, Università di Trento, 38123 Trento, Italy
E-mail:
Abstract: 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.
AMSclassification: primary 65M60; secondary 65M12, 53E10, 35K15.
Keywords: anisotropic curve shortening flow, finite element method, stability.
DOI: 10.5817/AM2023-3-263