UNCONDITIONALLY OPTIMAL ERROR ESTIMATES OF THE BILINEAR-CONSTANT SCHEME FOR TIME-DEPENDENT NAVIER-STOKES EQUATIONS  

作　　者：Huaijun Yang Dongyang Shi 

机构地区：[1]School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China [2]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China

出　　处：《Journal of Computational Mathematics》2022年第1期127-146,共20页计算数学（英文）

基　　金：supported by National Natural Science Foundation of China(No.11671369);the Doctoral Starting Foundation of Zhengzhou University of Aeronautics(No.63020390).

摘　　要：In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step restrictions.The analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial error.The τ-independent(τ is the time stepsize)error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L^(∞)-norm is bounded.Thus optimal error estimates can be obtained in a traditional way.Numerical results are provided to confirm the theoretical analysis.

关 键 词：Navier-Stokes equations Unconditionally optimal error estimates Bilinear-constant scheme Time-discrete system. 

分 类 号：O175[理学—数学]