Unconditional Optimal Error Estimates for the Transient Navier-Stokes Equations with Damping (Advances in Applied Mathematics and Mechanics, 2021)
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 ${L^∞}(L^2)$ and ${L^∞}(H^1)$, and the pressure in the norm ${L^∞}(L^2)$ are deduced. Finally, two numerical examples are provided to confirm the theoretical analysis.