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Lagrangian schemes for Wasserstein Gradient Flows
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Carrillo, Jose, Matthes, Daniel and Wolfram, Marie-Therese (2021) Lagrangian schemes for Wasserstein Gradient Flows. In: Wolfram, Marie-Therese, (ed.) Handbook of Numerical Analysis. Elsevier, pp. 271-311.
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Official URL: https://doi.org/10.1016/bs.hna.2020.10.002
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.
Item Type: | Book Item | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Publisher: | Elsevier | ||||||||
Book Title: | Handbook of Numerical Analysis | ||||||||
Editor: | Wolfram, Marie-Therese | ||||||||
Official Date: | 2021 | ||||||||
Dates: |
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Volume: | 22 | ||||||||
Page Range: | pp. 271-311 | ||||||||
DOI: | 10.1016/bs.hna.2020.10.002 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Copyright Holders: | Copyright © 2021 Elsevier B.V. All rights reserved. | ||||||||
Open Access Version: |
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