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Graph Gradient Flows

From Discrete to Continuum

Book Chapter (2026)
Author(s)

Yves van Gennip (TU Delft - Mathematical Physics)

Yoshikazu Giga (University of Tokyo)

Jun Okamoto (Institute for the Advanced Study of Human Biology)

Research Group
Mathematical Physics
DOI related publication
https://doi.org/10.1007/978-981-97-9812-4_2
More Info
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Publication Year
2026
Language
English
Research Group
Mathematical Physics
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository as part of the Taverne amendment. More information about this copyright law amendment can be found at https://www.openaccess.nl. Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. @en
Pages (from-to)
163-250
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

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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978-981-97-9812-4_2.pdf
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File under embargo until 02-03-2026