Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations
Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations
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DOI：
10.1007/s00211-015-0767-9
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发表时间：
2015-10
影响因子：
2.1
通讯作者：
Z. Si;Jilu Wang;Weiwei Sun
中科院分区：
文献类型：
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作者：
Z. Si;Jilu Wang;Weiwei Sun
研究了含时Navier-Stokes方程特征型方法的无条件稳定性和收敛性。我们提出了一个典型的修改特征有限元方法的最优误差估计，而以前的工作需要一定的时间步长的限制。该分析是基于一个迭代的特征时间离散系统，其中的误差函数被分为一个时间误差和一个空间误差。通过对特征时间离散系统的严格分析，证明了数值解与时间离散系统的解之间的差是无关的，其中的差表示时间步长。这样，数值解是有界的，用传统方法可以得到最优误差估计。数值结果证实了我们的分析，并清楚地显示了无条件稳定性和收敛性的修正特征有限元方法的时间依赖的Navier-Stokes方程。本文中使用的方法可以很容易地扩展到许多其他基于特征的方法。
The paper is concerned with the unconditional stability and convergence of characteristics type methods for the time-dependent Navier–Stokes equations. We present optimal error estimates inandnorms for a typical modified characteristics finite element method unconditionally, while all previous works require certain time-step restrictions. The analysis is based on an iterated characteristic time-discrete system, with which the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the difference between the numerical solution and the solution of the time-discrete system is-independent, wheredenotes the time stepsize. Thus numerical solution inis bounded and optimal error estimates can be obtained in a traditional way. Numerical results confirm our analysis and show clearly the unconditional stability and convergence of the modified characteristics finite element method for the time-dependent Navier–Stokes equations. The approach used in this paper can be easily extended to many other characteristics-based methods.