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

Mohammad Asadzadeh (Institutionen för matematiska vetenskaper, matematik) ; Piotr Kowalczyk
Advances in Computational Mathematics (1019-7168). Vol. 41 (2015), 4, p. 833-852.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2015-11-26. Senast ändrad 2016-07-07.
CPL Pubid: 226410

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur