Geodesic
Précision d'un schéma adaptatif semi-lagrangien pour l'équation de Vlasov
Martin Campos Pinto1
1 IGPM, RWTH, 56062 AACHEN, ALLEMAGNE
ESAIM. Proceedings, Tome 18 (2007), pp. 11-22.

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

In this talk, I present an adaptive semi-lagrangian scheme recently developed in collaboration with Michel Mehrenberger for approximating the solutions to the Vlasov-Poisson equation, and where the main feature consists in a new algorithm for transporting the multiscale meshes along the numerical flow. While reasonably simple, the algorithm we propose allows to transport “at first guess” the numerical solution to a given nonlinear transport problem, and the adaptive mesh on which this solution is computed. Moreover, this evolution is done in a way that is in some sense optimal, since on an analytical perspective, the accuracy of the solutions is established, together with a (still incomplete) bound on the complexity of the meshes. First proposed and analyzed in the article [3], then roughly described in a previous proceeding [5], this scheme was also given a detailed presentation in my PhD dissertation [4], in french. I shall here follow the latter and consider some “abstract”, Vlasov-type problem which properties will first be recalled. I will then describe our algorithm for transporting the multiscale meshes, and explain how its main properties enter the error analysis of the numerical scheme.
DOI : 10.1051/proc:071802

Martin Campos Pinto 1

1 IGPM, RWTH, 56062 AACHEN, ALLEMAGNE 
@article{EP_2007_18_a2,
     author = {Martin Campos Pinto},
     title = {Pr\'ecision d'un sch\'ema adaptatif semi-lagrangien pour l'\'equation de {Vlasov}},
     journal = {ESAIM. Proceedings},
     pages = {11--22},
     publisher = {mathdoc},
     volume = {18},
     year = {2007},
     doi = {10.1051/proc:071802},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:071802/}
}
TY  - JOUR
AU  - Martin Campos Pinto
TI  - Précision d'un schéma adaptatif semi-lagrangien pour l'équation de Vlasov
JO  - ESAIM. Proceedings
PY  - 2007
SP  - 11
EP  - 22
VL  - 18
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc:071802/
DO  - 10.1051/proc:071802
LA  - en
ID  - EP_2007_18_a2
ER  - 
%0 Journal Article
%A Martin Campos Pinto
%T Précision d'un schéma adaptatif semi-lagrangien pour l'équation de Vlasov
%J ESAIM. Proceedings
%D 2007
%P 11-22
%V 18
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/proc:071802/
%R 10.1051/proc:071802
%G en
%F EP_2007_18_a2
Martin Campos Pinto. Précision d'un schéma adaptatif semi-lagrangien pour l'équation de Vlasov. ESAIM. Proceedings, Tome 18 (2007), pp. 11-22. doi : 10.1051/proc:071802. http://geodesic.mathdoc.fr/articles/10.1051/proc:071802/

Cité par Sources :