We prove the convergence of discontinuous Galerkin approximations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials in velocity. To obtain stability properties, we introduce a suitable weighted L 2 space, with a time dependent weight and first prove global stability for the weighted L 2 norm and propagation of regularity. Then we prove error estimates between the numerical solution and the smooth solution to the Vlasov-Poisson system.

翻译：我们证明了Vlasov-Poisson系统不连续的Galerkin近似值的趋同性,这些近似值是用赫尔米特-波斯森(Hermite montinomials)的速度用双曲系统写成的。为了获得稳定性属性,我们引入了合适的加权L 2空间,有时间依赖权重,并首先证明加权L 2标准及常规性传播的全球稳定性。然后我们证明数字解决方案与Vlasov-波斯森系统平滑解决方案之间的误差估计值。