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Pré-Publication, Document De Travail Année : 2024

Discrete-to-continuous crystalline curvature flows

Résumé

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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Dates et versions

hal-04500307 , version 1 (11-03-2024)
hal-04500307 , version 2 (30-03-2024)

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Antonin Chambolle, Daniele de Gennaro, Massimiliano Morini. Discrete-to-continuous crystalline curvature flows. 2024. ⟨hal-04500307v1⟩
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