(untitled) (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.