Title :

Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker- Planck equations

Author(s) :

Dujardin, Guillaume [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Hérau, Frédéric [Auteur]
Laboratoire de Mathématiques Jean Leray [LMJL]
Lafitte-Godillon, Pauline [Auteur]
Mathématiques et Informatique pour la Complexité et les Systèmes [MICS]
Fédération de Mathématiques de CentraleSupélec

Journal title :

Numerische Mathematik

Publisher :

Springer Verlag

Publication date :

2020

ISSN :

0029-599X

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these dis-cretizations of velocity and space, we prove the ...
Show more >In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these dis-cretizations 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 Poincaré inequalities for a " two-direction " discretization of the derivative in velocity. For the inhomogeneous problem, we adapt hypocoercive methods to the discrete cases.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL