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Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem. (English) Zbl 1258.65084

From the authors’ abstract: Two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system are introduced and analyzed. The schemes are constructed by combining a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. Optimal error estimates in the case of smooth compactly supported initial data are given. A scheme that preserves the total energy of the system is also proposed.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
82D10 Statistical mechanics of plasmas
35Q83 Vlasov equations

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