Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system

Authors:	Nicolas Besse Michel Mehrenberger

Institution:	Institut de Recherche Mathematique Avancée, Université Louis Pasteur - CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France ; Institut de Recherche Mathematique Avancée, Université Louis Pasteur - CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France

Abstract:	In this paper we present some classes of high-order semi-Lagran- gian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that the distribution function and the electric field converge in the norm with a rate of $\displaystyle \mathcal{O}\left(\Delta t^2 +h^{m+1}+ \frac{h^{m+1}}{\Delta t}\right),$ where is the degree of the polynomial reconstruction, and $\Delta t$ and are respectively the time and the phase-space discretization parameters.

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