Entropy dissipation semi-discretization schemes for Fokker-Planck equations
Numerical Analysis
2017-12-20 v3
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.
Keywords
Cite
@article{arxiv.1608.02628,
title = {Entropy dissipation semi-discretization schemes for Fokker-Planck equations},
author = {Shui-Nee Chow and Luca Dieci and Wuchen Li and Haomin Zhou},
journal= {arXiv preprint arXiv:1608.02628},
year = {2017}
}