标题： 一种新的高阶一致分裂格式在纳维-斯托克斯方程中的稳定性与误差分析 显示英文标题

标题： Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations

摘要： 本文构造并分析了一类新的完全解耦的一致分裂格式用于纳维-斯托克斯方程。这些格式基于在$t^{n+\beta}$处的泰勒展开，其中$\beta\ge 1$是一个自由参数。结果显示，通过分别为二阶、三阶和四阶格式选择{\color{black} $\beta= 3, \,6,\,9$}，它们的数值解在强范数下是统一有界的，并且在二维和三维情况下都具有最优全局时间收敛速率。{\color{black}这些}结果是针对纳维-斯托克斯方程任何完全解耦的高于二阶格式的稳定性与收敛性的首次结果。数值结果表明，基于通常的BDF（即$\beta=1$）的三阶和四阶格式不是无条件稳定的，而具有适当$\beta$的新三阶和四阶格式是无条件稳定的，并且导致预期的收敛速率。 显示英文摘要

摘要： A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+\beta}$ with $\beta\ge 1$ being a free parameter. It is shown that by choosing {\color{black} $\beta= 3, \,6,\,9$} respectively for the second-, third- and fourth-order schemes, their numerical solutions are uniformed bounded in a strong norm, and admit optimal global-in-time convergence rates in both 2D and 3D. {\color{black}These } results are the first stability and convergence results for any fully decoupled, higher than second-order schemes for the Navier-Stokes equations. Numerical results are provided to show that the third- and fourth-order schemes based on the usual BDF (i.e. $\beta=1$) are not unconditionally stable while the new third- and fourth-order schemes with suitable $\beta$ are unconditionally stable and lead to expected convergence rates.