论文标题
关于弗拉索夫 - 波森系统的不连续的Galerkin/Hermite光谱方法的收敛性
On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system
论文作者
论文摘要
我们证明了使用Hermite多项式在速度中写成的双曲线系统，证明了vlasov-Poisson系统的不连续galerkin近似值的收敛性。为了获得稳定性，我们引入了一个合适的加权L 2空间，并具有时间相关的权重，并首先证明了加权L 2标准和规律性传播的全球稳定性。然后，我们证明了数值解和Vlasov-Poisson系统的平滑解决方案之间的错误估计。
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.
