Two-level iteration penalty methods for the incompressible flows

Abstract In this article, we present a new iteration penalty method for incompressible flows based on the iteration of pressure with a factor of penalty parameter, which was first developed for Stokes flows by Cheng and Abdul (2006) [14]. The stability and error estimates of numerical solutions in some norms are derived for this one-level method. Then, combining the techniques of two-level method and linearization with respect to the nonlinear convective term, we propose two-level Stokes/Oseen/Newton iteration penalty methods corresponding to three different linearization method, and show the stability and error estimates of these three methods. Finally, some numerical tests are given to demonstrate the effect of penalty parameter and the efficiency of the new methods.

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