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Convergence of the fully discrete JKO scheme

Year: 2026

Type: article

Abstract: The Jordan–Kinderlehrer–Otto (JKO) scheme provides a discrete-in-time approximation for the solutions of evolutionary equations with a Wasserstein gradient structure. We study a natural space-discretization of this scheme by restricting the minimization to the measures supported on the nodes of a regular grid. The study of the fully discrete JKO scheme is motivated by its applications to developing numerical schemes for the nonlinear diffusion equation with drift and for crowd motion models. The main result of this paper is the convergence of the scheme, as both the time and space discretization parameters tend to zero, in a suitable regime.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/drag053

Authors: Anastasiia Hraivoronska, Filippo Santambrogio

Institutions: Lyon 1 Université, École Centrale de Lyon, Centre National de la Recherche Scientifique, Institut Camille Jordan, Université Jean Monnet, Institut National des Sciences Appliquées de Lyon, Université Jean Monnet

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415098476

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