Iterative penalty methods for the steady Navier–Stokes equations

This paper presents one-level and two-level iterative penalty finite element methods to approximate the solutions of steady Navier–Stokes equations. First, one-level iterative penalty finite element method is applied to solve the steady Navier–Stokes equations numerically, and its H1H1 and L2L2 error estimates are derived. Then, two-level iterative penalty scheme is given and its error estimates are obtained for velocity and pressure. Finally, the numerical results are displayed to verify the theoretical analysis.