Précision d'un schéma adaptatif semi-lagrangien pour l'équation de Vlasov
ESAIM. Proceedings, Tome 18 (2007), pp. 11-22
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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.
@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},
year = {2007},
volume = {18},
doi = {10.1051/proc:071802},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:071802/}
}
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
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