@inbook{032d5a9f71c44197b6bf3004ea82e82d,
title = "Lagrangian schemes for Wasserstein gradient flows",
abstract = "This chapter reviews different numerical methods for specific examples of Wasserstein gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss discretizations of the parabolic-elliptic Keller-Segel model and of the fourth order thin film equation. The methods under review are of Lagrangian nature, that is, the numerical approximations trace the characteristics of the underlying transport equation rather than solving the evolution equation for the mass density directly. The two main approaches are based on integrating the equation for the Lagrangian maps on the one hand, and on solution of coupled ODEs for individual mass particles on the other hand.",
keywords = "Lagrangian discretization, Minimizing movement scheme, Wasserstein gradient flows",
author = "Carrillo, {Jose A.} and Daniel Matthes and Wolfram, {Marie Therese}",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2021",
month = jan,
doi = "10.1016/bs.hna.2020.10.002",
language = "English",
isbn = "9780444643056",
series = "Handbook of Numerical Analysis",
publisher = "Elsevier B.V.",
pages = "271--311",
editor = "Andrea Bonito and Nochetto, {Ricardo H.}",
booktitle = "Geometric Partial Differential Equations - Part II",
}