..We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for all the proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods
Ayuso De Dios, B., Carrillo, J., Shu, C. (2011). Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system. KINETIC AND RELATED MODELS, 4(4), 955-989 [10.3934/krm.2011.4.955].
Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system
Ayuso De Dios, B;
2011
Abstract
..We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for all the proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods
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