论文标题
Dahlquist，Liniger和Nevanlinna的可变步骤方法分析流体流动
Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow
论文作者
论文摘要
Dahlquist，Liniger和Nevanlinna提出的两步时间离散化是可变步骤$ G $ - 稳定的。 （相反，对于增加时间步骤，BDF2方法失去了$ A $稳定性，并且在近似解决方案中会遭受非物理能量的增长。）虽然未经探索，但它是Navier-Stokes方程式准确近似的理想选择。本报告将应用于NSE时，对方法的稳定性和收敛率进行了分析。事实证明，该方法是无条件，长时间稳定和二阶准确度的可变步骤。变量步骤错误估计也已得到证明。结果由几个数值测试支持。
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.
