Discrete hyperbolic curvature flow in the plane |
Klaus Deckelnick |
Tuesday, 2023-03-14 14:15 |
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Abstract: Hyperbolic curvature flow is a geometric evolution equation that in the plane can be viewed as the natural hyperbolic analogue of curve shortening flow. It was proposed by Gurtin and Podio-Guidugli to model certain wave phenomena in solid-liquid interfaces. We propose a semidiscrete finite difference method for the approximation of hyperbolic curvature flow and prove error bounds in natural norms. We also present numerical simulations, including the onset of singularities starting from smooth strictly convex initial data. This is joint work with Robert N\"urnberg (Trento). |