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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, in 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
Conference title
FVCA 9
Conference date
2020-06
Conference city
Bergen
Conference country
Norway
Book title
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
Book author
Dr. Robert Klöfkorn, Dr. Eirik Keilegavlen, Prof. Dr. Florin A. Radu, Prof. Jürgen Fuhrmann
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-030-43650-6
Pages
193-201
Publication identifier
Metadata
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Author(s)
Natale, Andrea
Laboratoire de Mathématiques d'Orsay [LMO]
Todeschi, Gabriele
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (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.
Subjects / Keywords
Energy diminishing scheme; Wasserstein gradient flows