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In this paper, we study two-level iteration penalty and variational multiscale method for the approximation of steady Navier-Stokes equations at high Reynolds number. Comparing with classical penalty method, this new method does not require very small penalty parameter ε. Moreover, two-level mesh method can save a large amount of CPU time. The error estimates in H norm for velocity and in L norm for pressure are derived. Finally, two numerical experiments are shown to support the efficiency of this new method.

TWO-LEVEL ITERATION PENALTY AND VARIATIONAL MULTISCALE METHOD FOR STEADY INCOMPRESSIBLE FLOWS