Discrete-to-continuum crystalline curvature flows

Antonin Chambolle; Daniele De Gennaro; Massimiliano Morini

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arXiv · 2403.04725

Discrete-to-continuum crystalline curvature flows

Antonin Chambolle·Daniele De Gennaro·Massimiliano Morini

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Abstract

We consider here a fully discrete variant of the implicit variational scheme for mean curvature flow [AlmTayWan,LucStu], in a setting where the flow is governed by a crystalline surface tension defined by the limit of pairwise interactions energy on the discrete grid. The algorithm is based on a new discrete distance from the evolving sets, which prevents the occurrence of the spatial drift and pinning phenomena identified in [MisiatsYip16,BraGelNov] in a similar discrete framework. We provide the first rigorous convergence result holding in any dimension, for any initial set and for a large class of purely crystalline anisotropies, in which the spatial discretization mesh can be of the same order or coarser than the time step.

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Antonin Chambolle, Daniele De Gennaro, Massimiliano Morini. 2024-03-07. Discrete-to-continuum crystalline curvature flows. https://arxiv.org/abs/2403.04725

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