TY - JOUR
T1 - Unconditionally Optimal Error Estimates of the Bilinear-Constant Scheme for Time-Dependent Navier-Stokes Equations
AU - Yang , Huaijun
AU - Shi , Dongyang
JO - Journal of Computational Mathematics
VL - 1
SP - 127
EP - 146
PY - 2021
DA - 2021/11
SN - 40
DO - http://doi.org/10.4208/jcm.2007-m2020-0164
UR - https://global-sci.org/intro/article_detail/jcm/19973.html
KW - Navier-Stokes equations, Unconditionally optimal error estimates, Bilinear-constant scheme, Time-discrete system.
AB - <p style="text-align: justify;">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 $\tau$-independent ($\tau$ 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 $L^{\infty}$-norm is bounded. Thus optimal error estimates can be obtained in a traditional way. Numerical results are provided to confirm the theoretical analysis.</p>