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TPFA Finite Volume Approximation of Wasserstein Gradient Flows

Natale, Andrea; Todeschi, Gabriele (2020), TPFA Finite Volume Approximation of Wasserstein Gradient Flows, dans Dr. Robert Klöfkorn, Dr. Eirik Keilegavlen, Prof. Dr. Florin A. Radu, Prof. Jürgen Fuhrmann, Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, Springer : Berlin Heidelberg, p. 193-201. 10.1007/978-3-030-43651-3_16

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Type
Communication / Conférence
Date
2020
Titre du colloque
FVCA 9
Date du colloque
2020-06
Ville du colloque
Bergen
Pays du colloque
Norway
Titre de l'ouvrage
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
Auteurs de l’ouvrage
Dr. Robert Klöfkorn, Dr. Eirik Keilegavlen, Prof. Dr. Florin A. Radu, Prof. Jürgen Fuhrmann
Éditeur
Springer
Ville d’édition
Berlin Heidelberg
Isbn
978-3-030-43650-6
Pages
193-201
Identifiant publication
Métadonnées
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Auteur(s)
Natale, Andrea
Laboratoire de Mathématiques d'Orsay [LMO]
Todeschi, Gabriele
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Flux Approximation Finite Volume schemes discretizing such problems which preserve the variational structure and have second order accuracy in space. We propose an interior point method to solve the discrete variational problem, providing an efficient and robust algorithm. We present two applications to test the scheme and show its order of convergence.
Mots-clés
Energy diminishing scheme; Wasserstein gradient flows