--- res: bibo_abstract: - We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Dominik L foaf_name: Forkert, Dominik L foaf_surname: Forkert foaf_workInfoHomepage: http://www.librecat.org/personId=35C79D68-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Jan foaf_name: Maas, Jan foaf_surname: Maas foaf_workInfoHomepage: http://www.librecat.org/personId=4C5696CE-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0845-1338 - foaf_Person: foaf_givenName: Lorenzo foaf_name: Portinale, Lorenzo foaf_surname: Portinale foaf_workInfoHomepage: http://www.librecat.org/personId=30AD2CBC-F248-11E8-B48F-1D18A9856A87 bibo_doi: 10.1137/21M1410968 bibo_issue: '4' bibo_volume: 54 dct_date: 2022^xs_gYear dct_identifier: - UT:000889274600001 dct_isPartOf: - http://id.crossref.org/issn/0036-1410 - http://id.crossref.org/issn/1095-7154 dct_language: eng dct_publisher: Society for Industrial and Applied Mathematics@ dct_subject: - Fokker--Planck equation - gradient flow - evolutionary $\Gamma$-convergence dct_title: Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions@ ...