Convergence analysis for Backward-Euler and mixed discontinuous Galerkin methods for the Vlasov-Poisson system .
Journal article, 2015

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.


Mohammad Asadzadeh

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Piotr Kowalczyk

University of Warsaw

Advances in Computational Mathematics

1019-7168 (ISSN) 1572-9044 (eISSN)

Vol. 41 4 833-852

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Basic sciences



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