---
_id: '10022'
abstract:
- lang: eng
  text: We consider finite-volume approximations of Fokker-Planck equations on bounded
    convex domains in 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 Γ-convergence, i.e., we pass to the limit at the level
    of the gradient flow structures, generalising 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.
acknowledgement: This work is supported by the European Research Council (ERC) under
  the European Union’s Horizon 2020 research and innovation programme (grant agreement
  No 716117) and by the Austrian Science Fund (FWF), grants No F65 and W1245.
article_number: '2008.10962'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dominik L
  full_name: Forkert, Dominik L
  id: 35C79D68-F248-11E8-B48F-1D18A9856A87
  last_name: Forkert
- first_name: Jan
  full_name: Maas, Jan
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
- first_name: Lorenzo
  full_name: Portinale, Lorenzo
  id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
  last_name: Portinale
citation:
  ama: Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient
    flow structures for Fokker-Planck equations in multiple dimensions. <i>arXiv</i>.
    doi:<a href="https://doi.org/10.48550/arXiv.2008.10962">10.48550/arXiv.2008.10962</a>
  apa: Forkert, D. L., Maas, J., &#38; Portinale, L. (n.d.). Evolutionary Γ-convergence
    of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
    <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2008.10962">https://doi.org/10.48550/arXiv.2008.10962</a>
  chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary Γ-Convergence
    of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
    <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2008.10962">https://doi.org/10.48550/arXiv.2008.10962</a>.
  ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary Γ-convergence of entropic
    gradient flow structures for Fokker-Planck equations in multiple dimensions,”
    <i>arXiv</i>. .
  ista: Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient
    flow structures for Fokker-Planck equations in multiple dimensions. arXiv, 2008.10962.
  mla: Forkert, Dominik L., et al. “Evolutionary Γ-Convergence of Entropic Gradient
    Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>ArXiv</i>,
    2008.10962, doi:<a href="https://doi.org/10.48550/arXiv.2008.10962">10.48550/arXiv.2008.10962</a>.
  short: D.L. Forkert, J. Maas, L. Portinale, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-09-17T10:57:27Z
date_published: 2020-08-25T00:00:00Z
date_updated: 2026-04-08T07:00:03Z
day: '25'
department:
- _id: JaMa
doi: 10.48550/arXiv.2008.10962
ec_funded: 1
external_id:
  arxiv:
  - '2008.10962'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2008.10962
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
  record:
  - id: '11739'
    relation: later_version
    status: public
  - id: '10030'
    relation: dissertation_contains
    status: public
status: public
title: Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck
  equations in multiple dimensions
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2020'
...