A variational finite volume scheme for Wasserstein gradient flows
Sign Up to like & getrecommendations! Published in 2020 at "Numerische Mathematik"
DOI: 10.1007/s00211-020-01153-9
Abstract: We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula, whereas space… read more here.
Keywords: finite volume; gradient flows; scheme; wasserstein gradient ... See more keywords
Local convergence rates for Wasserstein gradient flows and McKean-Vlasov equations with multiple stationary solutions
Sign Up to like & getrecommendations! Published in 2024 at "Probability Theory and Related Fields"
DOI: 10.1007/s00440-025-01399-0
Abstract: Non-linear versions of log-Sobolev inequalities, that link a free energy to its dissipation along the corresponding Wasserstein gradient flow (i.e. corresponds to Polyak-Lojasiewicz inequalities in this context), are known to provide global exponential long-time convergence… read more here.
Keywords: free energy; stationary solutions; convergence rates; wasserstein gradient ... See more keywords