An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Analysis of PDEs
2017-03-23 v1 Optimization and Control
Abstract
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
Cite
@article{arxiv.1703.07709,
title = {An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations},
author = {Adriano Festa and Diogo A. Gomes and Roberto M. Velho},
journal= {arXiv preprint arXiv:1703.07709},
year = {2017}
}
Comments
14 pages, 8 figures