Two-level stabilized method based on Newton iteration for the steady Smagorinsky model

A combination method of the Newton iteration and the two-level stabilized finite element algorithm based on local Gauss integration is constructed for solving numerically the steady Smagorinsky model. This algorithm involves solving one small, nonlinear coarse mesh with mesh size HH and two linear problems on the fine mesh with mesh size hh. Based on the stabilized method and the Newton two-level technique, the computation will be more effective and convenient and the scaling between HH and hh becomes h=O(H4)h=O(H4), which greatly complements the results of Borggaard et al. (2008) [2]. Moreover, the stability and convergence of the two-level Newton iterative solution are analyzed. Finally, some numerical tests are made to demonstrate the effectiveness of the given method.