流体流动的Dahlquist，Liniger和Nevanlinna变步长方法分析
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow
摘要：
Dahlquist，Liniger和Nevanlinna提出的两步时间离散方法是变步长$G$稳定的。(In相反，对于增加的时间步长，BDF 2方法失去了$A$稳定性，并且在近似解中遭受非物理能量增长。）虽然还未被探索，但它是理想的Navier-斯托克斯方程的时间精确近似。本报告提出了一个分析，为可变的时间步长，该方法的稳定性和收敛速度时，适用于NSE。证明了该方法具有变步长、无条件、长时间稳定和二阶精度等优点。变步长误差估计也被证明。结果得到了几个数值试验的支持。
英文摘要：
The two-step time discretization proposed by Dahlquist, Liniger and Nevanlinna is variable step $G$-stable. (In contrast, for increasing time steps, the BDF2 method loses $A$-stability and suffers non-physical energy growth in the approximate solution.) While unexplored, it is thus ideal for time accurate approximation of the Navier-Stokes equations. This report presents an analysis, for variable time-steps, of the method's stability and convergence rates when applied to the NSE. It is proven that the method is variable step, unconditionally, long time stable and second order accurate. Variable step error estimates are also proven. The results are supported by several numerical tests.
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