An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

2017/03/22 by Adriano Festa, Festa, Adriano, Diogo A. Gomes +3
Decision Sciences · Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1703.07709

openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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