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DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM
Preview AbstractWe introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov–Poisson system. 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. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.