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Convergence analysis for Backward-Euler and mixed discontinuous Galerkin methods for the Vlasov-Poisson system

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Abstract

We construct and analyze a numerical scheme for the two-dimensional Vlasov-Poisson system based on a backward-Euler (BE) approximation in time combined with a mixed finite element method for a discretization of the Poisson equation in the spatial domain and a discontinuous Galerkin (DG) finite element approximation in the phase-space variables for the Vlasov equation. We prove the stability estimates and derive the optimal convergence rates depending upon the compatibility of the finite element meshes, used for the discretizations of the spatial variable in Poisson (mixed) and Vlasov (DG) equations, respectively. The error estimates for the Poisson equation are based on using Brezzi-Douglas-Marini (BDM) elements in L 2 and H −s, s>0, norms.

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Authors and Affiliations

  1. Department of Mathematics, Chalmers University of Technology and University of Gothenburg, SE–412 96, Göteborg, Sweden

    Mohammad Asadzadeh

  2. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Piotr Kowalczyk

Authors
  1. Mohammad Asadzadeh
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  2. Piotr Kowalczyk
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Correspondence to Mohammad Asadzadeh.

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Communicated by: Alexander Barnett

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Asadzadeh, M., Kowalczyk, P. Convergence analysis for Backward-Euler and mixed discontinuous Galerkin methods for the Vlasov-Poisson system. Adv Comput Math 41, 833–852 (2015). https://doi.org/10.1007/s10444-014-9388-6

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  • DOI: https://doi.org/10.1007/s10444-014-9388-6

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