TY - JOUR
T1 - Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping
AU - Li , Minghao
AU - Li , Zhenzhen
AU - Shi , Dongyang
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 248
EP - 274
PY - 2021
DA - 2021/11
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2020-0239
UR - https://global-sci.org/intro/article_detail/aamm/19984.html
KW - Navier-Stokes equations with damping, linearized backward Euler scheme, error splitting technique, unconditional optimal error estimates.
AB - <p style="text-align: justify;">In this paper, the transient Navier-Stokes equations with damping are considered. Firstly, the semi-discrete scheme is discussed and optimal error estimates are derived. Secondly, a linearized backward Euler scheme is proposed. By the error split technique, the Stokes operator and the $H^{-1}$-norm estimate, unconditional optimal error estimates for the velocity in the norms ${L^\infty}(L^2)$ and ${L^\infty}(H^1)$, and the pressure in the norm ${L^\infty}(L^2)$ are deduced. Finally, two numerical examples are provided to confirm the theoretical analysis.</p>