---
_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
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. arXiv.
apa: Forkert, D. L., Maas, J., & Portinale, L. (n.d.). Evolutionary Γ-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
arXiv.
chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary Γ-Convergence
of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
ArXiv, n.d.
ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary Γ-convergence of entropic
gradient flow structures for Fokker-Planck equations in multiple dimensions,”
arXiv. .
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.” ArXiv,
2008.10962.
short: D.L. Forkert, J. Maas, L. Portinale, ArXiv (n.d.).
date_created: 2021-09-17T10:57:27Z
date_published: 2020-08-25T00:00:00Z
date_updated: 2023-09-07T13:31:05Z
day: '25'
department:
- _id: JaMa
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
page: '33'
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: submitted
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...