On Error Estimates of the Penalty Method for Unsteady Navier–Stokes Equations

The penalty method has been widely used for numerical computations of the unsteady Navier–Stokes equations. However, the best error estimates available to the author’s knowledge were not optimal and could have led to an improper choice of the penalty coefficient ε for time discretizations of the penalized system. Optimal error estimates for the penalized system and its time discretizations for the unsteady Navier–Stokes equations are derived.