Interpretation of Finite Volume discretization schemes for the Fokker Planck equation as gradient flows for the discrete Wasserstein distance

F Al Reda (1) , B Maury (1, 2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 DMA - Département de Mathématiques et Applications - ENS Paris

This paper establishes a link between some space discretization strategies of the Finite Volume type for the Fokker-Planck equation in general meshes (Voronoï tesselations) and gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein distances on graphs recently proposed by Maas [6].

Mots clés: Gradient flows; Wasserstein distance; Finites Volumes discretization; Fokker-Planck equation; Heat equation; Resistive Network; Markov Kernel

Domaines: Analyse numérique [math.NA]

F Al Reda, B Maury. Interpretation of Finite Volume discretization schemes for the Fokker Planck equation as gradient flows for the discrete Wasserstein distance. 2016. ⟨hal-01288983⟩