TY - CHAP
T1 - An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems
AU - Festa, Adriano
AU - Gomes, Diogo A.
AU - Machado Velho, Roberto
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-CRG2017-3452
Acknowledgements: The author “D. Gomes” was partially supported by KAUST baseline and start-up funds and by KAUST OSR-CRG2017-3452. The author “A. Festa” was partially supported by the Haute-Normandie Regional Council via the M2NUM project.
PY - 2018/12/23
Y1 - 2018/12/23
N2 - 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 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.
AB - 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 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.
UR - http://hdl.handle.net/10754/631173
UR - https://link.springer.com/chapter/10.1007%2F978-3-030-01947-1_4
UR - http://www.scopus.com/inward/record.url?scp=85059091111&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-01947-1_4
DO - 10.1007/978-3-030-01947-1_4
M3 - Chapter
SN - 9783030019464
SP - 73
EP - 92
BT - PDE Models for Multi-Agent Phenomena
PB - Springer Nature
ER -