Numerical schemes for the aggregation equation with pointy potentials

Benoît Fabrèges; Hélène Hivert; Kevin Le Balc’h; Sofiane Martel; François Delarue; Frédéric Lagoutière; Nicolas Vauchelet

doi:10.1051/proc/201965384

Geodesic

Parcourir par

Numerical schemes for the aggregation equation with pointy potentials

Benoît Fabrèges ¹ ; Hélène Hivert ² ; Kevin Le Balc’h ³ ; Sofiane Martel ⁴ ; François Delarue ⁵ ; Frédéric Lagoutière ¹ ; Nicolas Vauchelet ⁶

¹ Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France
² Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully, France
³ Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
⁴ Laboratoire d’hydraulique Saint-Venant (École des Ponts ParisTech – EDF R&D – CEREMA), Université Paris-Est, 6 quai Watier, 78401 Chatou Cedex, France
⁵ Laboratoire J.-A. Dieudonné, UMR CNRS 7351, Univ. Nice, Parc Valrose, 06108 Nice Cedex 02, France
⁶ Université Paris 13, Sorbonne Paris Cité, CNRS UMR 7539, Laboratoire Analyse Géométrie et Applications, 93430 Villetaneuse, France

ESAIM. Proceedings, Tome 65 (2019), pp. 384-400.

Voir la notice de l'article provenant de la source EDP Sciences

Résumé

The aggregation equation is a nonlocal and nonlinear conservation law commonly used to describe the collective motion of individuals interacting together. When interacting potentials are pointy, it is now well established that solutions may blow up in finite time but global in time weak measure valued solutions exist. In this paper we focus on the convergence of particle schemes and finite volume schemes towards these weak measure valued solutions of the aggregation equation.

DOI : 10.1051/proc/201965384

Affiliations des auteurs :

Benoît Fabrèges ¹ ; Hélène Hivert ² ; Kevin Le Balc’h ³ ; Sofiane Martel ⁴ ; François Delarue ⁵ ; Frédéric Lagoutière ¹ ; Nicolas Vauchelet ⁶

@article{EP_2019_65_a16,
     author = {Beno{\^\i}t Fabr\`eges and H\'el\`ene Hivert and Kevin Le Balc{\textquoteright}h and Sofiane Martel and Fran\c{c}ois Delarue and Fr\'ed\'eric Lagouti\`ere and Nicolas Vauchelet},
     title = {Numerical schemes for the aggregation equation with pointy potentials},
     journal = {ESAIM. Proceedings},
     pages = {384--400},
     publisher = {mathdoc},
     volume = {65},
     year = {2019},
     doi = {10.1051/proc/201965384},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965384/}
}

TY  - JOUR
AU  - Benoît Fabrèges
AU  - Hélène Hivert
AU  - Kevin Le Balc’h
AU  - Sofiane Martel
AU  - François Delarue
AU  - Frédéric Lagoutière
AU  - Nicolas Vauchelet
TI  - Numerical schemes for the aggregation equation with pointy potentials
JO  - ESAIM. Proceedings
PY  - 2019
SP  - 384
EP  - 400
VL  - 65
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201965384/
DO  - 10.1051/proc/201965384
LA  - en
ID  - EP_2019_65_a16
ER  -

%0 Journal Article
%A Benoît Fabrèges
%A Hélène Hivert
%A Kevin Le Balc’h
%A Sofiane Martel
%A François Delarue
%A Frédéric Lagoutière
%A Nicolas Vauchelet
%T Numerical schemes for the aggregation equation with pointy potentials
%J ESAIM. Proceedings
%D 2019
%P 384-400
%V 65
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201965384/
%R 10.1051/proc/201965384
%G en
%F EP_2019_65_a16

Benoît Fabrèges; Hélène Hivert; Kevin Le Balc’h; Sofiane Martel; François Delarue; Frédéric Lagoutière; Nicolas Vauchelet. Numerical schemes for the aggregation equation with pointy potentials. ESAIM. Proceedings, Tome 65 (2019), pp. 384-400. doi : 10.1051/proc/201965384. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965384/

Cité par Sources :