Titre :

Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations

Auteur(s) :

Bailo, Rafael [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Carrillo, José [Auteur]
Mathematical Institute [Oxford] [MI]
Murakawa, Hideki [Auteur]
Ryukoku University
Schmidtchen, Markus [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]

Titre de la revue :

Mathematical Models and Methods in Applied Sciences

Pagination :

2487-2522

Éditeur :

World Scientific Publishing

Date de publication :

2020

ISSN :

0218-2025

Mot(s)-clé(s) en anglais :

Finite-volume methods
convergence of numerical methods
drift-diffusion equations
integro-differential equations

Discipline(s) HAL :

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

Résumé en anglais : [en]

We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced in [3]. Crucially, this scheme keeps the dissipation property ...
Lire la suite >We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced in [3]. Crucially, this scheme keeps the dissipation property of an associated fully discrete energy, and does so unconditionally with respect to the time step. Our main contribution in this work is to show the convergence of the method under suitable assumptions on the diffusion functions and potentials involved.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet Européen :

New mathematical tools to uncover the complex dynamics of many-body systems

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL