@Article{JCM-40-1,
author = {Yang, Huaijun and Shi, Dongyang},
title = {Unconditionally Optimal Error Estimates of the Bilinear-Constant Scheme for Time-Dependent Navier-Stokes Equations},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {1},
pages = {127--146},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2007-m2020-0164},
url = {https://global-sci.com/article/84172/unconditionally-optimal-error-estimates-of-the-bilinear-constant-scheme-for-time-dependent-navier-stokes-equations}
}