Convergence of a linearly transformed particle method for aggregation equations
File(s)CamposPinto2018_Article_ConvergenceOfALinearlyTransfor.pdf (1.58 MB)
Published version
Author(s)
Carrillo de la Plata, J
Campos-Pinto, Martin
Charles, Frederique
Choi, Young-Pil
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.
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.
Date Issued
2018-08-01
Date Acceptance
2018-03-05
Citation
Numerische Mathematik, 2018, 139 (4), pp.743-793
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
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P031587/1
Subjects
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
Date Publish Online
2018-04-11