On Error Estimates of the Pressure-Correction Projection Methods for the Time-Dependent Navier-Stokes Equations

Abstract

In this paper, we present a new pressure-correction projection scheme for solving the time-dependent Navier-Stokes equations, which is based on the Crank-Nicolson extrapolation method in the time discretization. Error estimates for the velocity and the pressure of semidiscretized scheme are derived by interpreting the projection scheme as second-order time discretization of a perturbed system which approximates the incompressible Navier-Stokes equations.