A fully discrete variational scheme for solving nonlinear Fokker-Planck equations in multiple space dimensions

Oliver Junge, Daniel Matthes, Horst Osberger

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multidimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a gradient flow of an entropy functional in the L2 - Wasserstein metric; the second is the Lagrangian nature, meaning that solutions can be written as the push-forward transformation of the initial density under suitable flow maps. The resulting numerical scheme is entropy diminishing and mass conserving. Further, we are able to prove consistency in the sense that if the discrete solutions are regular independently of the mesh size, then they converge to a classical solution. Finally, we present results from numerical experiments in space dimension d = 2.

Original languageEnglish
Pages (from-to)419-423
Number of pages5
JournalSIAM Journal on Numerical Analysis
Volume55
Issue number1
DOIs
StatePublished - 2017

Keywords

  • Fokker-Planck equation
  • Gradient flow
  • Lagrangian discretization
  • Structure preservation
  • Wasserstein metric

Fingerprint

Dive into the research topics of 'A fully discrete variational scheme for solving nonlinear Fokker-Planck equations in multiple space dimensions'. Together they form a unique fingerprint.

Cite this