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Convergence of a linearly transformed particle method for aggregation equations

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Title: Convergence of a linearly transformed particle method for aggregation equations
Authors: Carrillo de la Plata, J
Campos-Pinto, M
Charles, F
Choi, Y-P
Item Type: Journal Article
Abstract: We study a linearly transformed particle method for the aggre- gation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in L 1 and L ∞ norms de- pending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in L 1 ∩ L p norm.
Issue Date: 1-Aug-2018
Date of Acceptance: 5-Mar-2018
URI: http://hdl.handle.net/10044/1/57851
DOI: https://dx.doi.org/10.1007/s00211-018-0958-2
ISSN: 0029-599X
Publisher: Springer Verlag
Start Page: 743
End Page: 793
Journal / Book Title: Numerische Mathematik
Volume: 139
Issue: 4
Copyright Statement: © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
NONLOCAL INTERACTION EQUATIONS
INTERACTION ENERGY
STATIONARY STATES
VORTEX METHODS
LOCAL MINIMIZERS
GRANULAR MEDIA
POTENTIALS
STABILITY
MODEL
FLOW
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
Numerical & Computational Mathematics
Publication Status: Published
Online Publication Date: 2018-04-11
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences