Archivio Istituzionale della RicercaHere, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of HamiltonJacobi (HJ) equations. Using this structure, we show how to transfer properties of schemes for HJ equations to 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
An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems / Festa, A.; Gomes, D. A.; Velho, R. M. (SPRINGER INDAM SERIES). - In: PDE Models for Multi-Agent Phenomena[s.l] : Springer International Publishing, 2018. - ISBN 978-3-030-01946-4. - pp. 73-92 [10.1007/978-3-030-01947-1_4]
An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems
Festa A.;
2018
Abstract
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of HamiltonJacobi (HJ) equations. Using this structure, we show how to transfer properties of schemes for HJ equations to 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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https://hdl.handle.net/11583/2786297