On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system

Autor:	Bessemoulin-Chatard, Marianne, Filbet, Francis
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jcp.2021.110881
Popis:	We study a class of spatial discretizations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials. In particular, we focus on spectral methods and discontinuous Galerkin approximations. To obtain L 2 stability properties, we introduce a new L 2 weighted space, with a time dependent weight. For the Hermite spectral form of the Vlasov-Poisson system, we prove conservation of mass, momentum and total energy, as well as global stability for the weighted L 2 norm. These properties are then discussed for several spatial discretizations. Finally, numerical simulations are performed with the proposed DG/Hermite spectral method to highlight its stability and conservation features. Comment: arXiv admin note: text overlap with arXiv:2004.02685
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2106.07468 Zobrazit plný text záznamu View this record from Arxiv