As on arXiv
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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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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A distributional approach to nonlocal curvature flows
Topics Anisotropic & nonlocal flows, Other curvature flows · Same author Massimiliano Morini · Shared terms “crystalline”
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Elementary discrete diffusion/redistancing schemes for the mean curvature flow
Topics Mean curvature flow · Same authors Antonin Chambolle, Daniele De Gennaro, Massimiliano Morini · Shared terms “fully discrete”, “discretization”
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Variational Nonlinear and Nonlocal Curvature Flows
Topics Anisotropic & nonlocal flows, Other curvature flows · Same author Daniele De Gennaro
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Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions
Topics Anisotropic & nonlocal flows, Other curvature flows · Shared terms “crystalline”, “anisotropy”
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Area-preserving crystalline curvature flow in two dimensions
Topics Anisotropic & nonlocal flows, Other curvature flows · Shared terms “crystalline curvature”
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Minimizing Movements for Anisotropic and Inhomogeneous Mean Curvature Flows
Topics Mean curvature flow · Same authors Antonin Chambolle, Daniele De Gennaro, Massimiliano Morini
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Threshold dynamics approximation schemes for anisotropic mean curvature flows with a forcing term
Topics Anisotropic & nonlocal flows · Shared terms “initial set”
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Graphical translators for anisotropic and crystalline mean curvature flow
Topics Anisotropic & nonlocal flows · Shared terms “crystalline”, “anisotropy”
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.