Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations
Numerical Analysis
2018-02-08 v1
Abstract
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence to the equilibrium of the solutions, for time-continuous equations as well as for time-discrete equations. Our method uses new types of discrete Poincar\'e inequalities for a "two-direction" discretization of the derivative in velocity. For the inhomogeneous problem, we adapt hypocoercive methods to the discrete cases.
Cite
@article{arxiv.1802.02173,
title = {Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equations},
author = {Guillaume Dujardin and Frédéric Hérau and Pauline Lafitte},
journal= {arXiv preprint arXiv:1802.02173},
year = {2018}
}