Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions

Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv, 2008.10962.

Preprint | Submitted | English
Department
Abstract
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.
Publishing Year
Date Published
2020-08-25
Journal Title
arXiv
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
Page
33
IST-REx-ID

Cite this

Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv.
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.
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.
D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” arXiv. .
Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. arXiv, 2008.10962.
Forkert, Dominik L., et al. “Evolutionary Γ-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” ArXiv, 2008.10962.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 2008.10962

Search this title in

Google Scholar