Entropy dissipation semi-discretization schemes for Fokker-Planck equations

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. We discretize the underlying state by a finite graph and define a discrete 2-Wasserstein metric. Based on such metric, we introduce a dynamical system, which is a gradient flow of the discrete free energy. We prove that the new 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.

References in corpus (2)

• A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
• Numerical Study of a Particle Method for Gradient Flows

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