Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, to appear in J. Comp. Phys.

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Title: Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, to appear in J. Comp. Phys.
Author(s): Carrillo de la Plata, J
Ranetbauer, H
Wolfram, MT
Item Type: Journal Article
Abstract: In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient ow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient ow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi- discrete scheme are guaranteed by its construction. We illustrate this properties with various examples in spatial dimension one and two.
Publication Date: 22-Sep-2016
Date of Acceptance: 17-Sep-2016
URI: http://hdl.handle.net/10044/1/41894
DOI: https://dx.doi.org/10.1016/j.jcp.2016.09.040
ISSN: 1090-2716
Publisher: Elsevier
Start Page: 186
End Page: 202
Journal / Book Title: Journal of Computational Physics
Volume: 327
Copyright Statement: © 2016 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: The Royal Society
Funder's Grant Number: WM120001
Keywords: Applied Mathematics
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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