We 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
Ayuso De Dios, B., Carrillo, J., Shu, C. (2012). Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 22(12), 1-45 [10.1142/S021820251250042X].
Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem
Ayuso De Dios, B
;
2012
Abstract
We 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
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