ON THE CONVERGENCE OF DISCONTINUOUS GALERKIN/HERMITE SPECTRAL METHODS FOR THE VLASOV-POISSON SYSTEM

被引：4

作者：

Bessemoulin-Chatard, Marianne ^{[1
]}

Filbet, Francis ^{[2
]}

机构：

[1] Nantes Univ, CNRS, Lab Math Jean Leray, UMR6629 2, F-44322 Nantes 3, France

[2] Univ Paul Sabatier, Inst Math Toulouse, UMR5219, F-31062 Toulouse, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2023年 / 61卷 / 04期

关键词：

convergence; discontinuous Galerkin method; Hermite spectral method; Vlasov-Poisson; FINITE-ELEMENT CODE; NUMERICAL-INTEGRATION; SIMULATION; CONSERVATION; PROPAGATION; EQUATIONS; SCHEMES; PLASMAS; BEAMS;

D O I：

10.1137/22M1518232

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the convergence of discontinuous Galerkin approximations for the VlasovPoisson system written as a hyperbolic system using Hermite polynomials in velocity. To obtain stability properties, we introduce a suitable weighted L2 space, with a time-dependent weight, and first prove global stability for the weighted L2 norm and propagation of regularity. Then we prove error estimates between the numerical solution and the smooth solution to the Vlasov-Poisson system.

引用

页码：1664 / 1688

页数：25

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