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This paper gives a framework to study a continuum limit of a gradient flow on a graph where the number of vertices increases in an appropriate way. As examples, we prove the convergence of a discrete total variation flow and a discrete Allen–Cahn flow on discretised tori to their respective continuum limits.

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Graph Gradient Flows: From Discrete to Continuum

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  • 发表日期：

    2026年

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  • Yves van Gennip,
  • Yoshikazu Giga,
  • Jun Okamoto

摘要

This paper gives a framework to study a continuum limit of a gradient flow on a graph where the number of vertices increases in an appropriate way. As examples, we prove the convergence of a discrete total variation flow and a discrete Allen–Cahn flow on discretised tori to their respective continuum limits.