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.
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
@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/}
}
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