论文标题
多维可压缩纳维尔 - 斯托克斯系统的有限差异方案的收敛性和误差估计
Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system
论文作者
论文摘要
我们证明了可压缩的Navier的有限差近似 - 在$ r^d，$ $ d = 2,3，绝热系数$γ> 1 $中的有限差近似。采用相对能量功能，我们发现收敛速率是\ emph {roniform}，就$γ\ geq d/2 $的离散参数而言。所有结果都是\ emph {无条件}的意义，即我们对数值解决方案的规律性或有限性没有假设。我们还提供数值实验来验证理论收敛速率。据我们所知，这项工作包含第一个无条件的结果，即对不稳定可压缩的纳维尔的有限差分方案的收敛性 - 在多个维度上stokes System。
We prove convergence of a finite difference approximation of the compressible Navier--Stokes system towards the strong solution in $R^d,$ $d=2,3,$ for the adiabatic coefficient $γ>1$. Employing the relative energy functional, we find a convergence rate which is \emph{uniform} in terms of the discretization parameters for $γ\geq d/2$. All results are \emph{unconditional} in the sense that we have no assumptions on the regularity nor boundedness of the numerical solution. We also provide numerical experiments to validate the theoretical convergence rate. To the best of our knowledge this work contains the first unconditional result on the convergence of a finite difference scheme for the unsteady compressible Navier--Stokes system in multiple dimensions.
