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Entropy Dissipation Semi-Discretization Schemes for Fokker–Planck Equations

  • Shui-Nee Chow
  • Luca Dieci
  • Wuchen Li
  • Haomin Zhou
Article
  • 52 Downloads

Abstract

We propose a new semi-discretization scheme to approximate nonlinear Fokker–Planck equations, by exploiting the gradient flow structures with respect to the 2-Wasserstein metric in the space of probability densities. We discretize the underlying state by a finite graph and define a discrete 2-Wasserstein metric in the discrete probability space. Based on such metric, we introduce a gradient flow of the discrete free energy as semi discretization scheme. We prove that the scheme maintains dissipativity of the free energy and converges to a discrete Gibbs measure at exponential dissipation rate. We exhibit these properties on several numerical examples.

Keywords

Fokker–Planck equation Optimal transport Entropy dissipation Numerics 

Mathematics Subject Classification

65L07 65L12 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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