Preprint

Inserted: 7 mar 2024
Last Updated: 7 mar 2024

Year: 2024

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 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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• DiscreteCrystal.pdf