Entropy dissipation semi-discretization schemes for Fokker-Planck equations

18 Dec 2017  ·  Chow Shui-Nee, Dieci Luca, Li Wuchen, Zhou Haomin ·

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. read more

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Numerical Analysis