Title :

On a structure-preserving numerical method for fractional Fokker-Planck equations

Author(s) :

Ayi, Nathalie [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Hivert, Hélène [Auteur]
Institut Camille Jordan [ICJ]
Modélisation mathématique, calcul scientifique [MMCS]
Tristani, Isabelle [Auteur]
Département de Mathématiques et Applications - ENS-PSL [DMA]

Journal title :

Mathematics of Computation

Pages :

635--693

Publisher :

American Mathematical Society

Publication date :

2023

ISSN :

0025-5718

English keyword(s) :

Fractional Laplacian
Kinetic equations
Numerical methods
Hypocoercivity

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic Lévy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as ...
Show more >In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic Lévy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of mass, heavy-tailed equilibrium and (hypo)coercivity properties. We perform a thorough analysis of the numerical scheme and show exponential stability and convergence of the scheme. Along the way, we introduce new tools of discrete functional analysis, such as discrete nonlocal Poincaré and interpolation inequalities adapted to fractional diffusion. Our theoretical findings are illustrated and complemented with numerical simulations..Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Entropie, flots, inégalités
Singularités dans des limites asymptotiques d'équations de Vlasov

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL