Two-level Method Based on Newton Iteration for the Stationary Navier-Stokes Equations

This paper propose and analyze the two-level stabilized finite element method for the stationary Navier-Stokes equations based on Newon iteration. This algorithm involves solving one small, nonlinear coarse mesh with mesh size H and two linear problems on the fine mesh with mesh size h. Based on local Gauss integration and the quadratic equal-order triangular element ,the two-level stabilized method our study provide an approximate solution ( ) , h h u p with convergence rate of same order as the approximate solution ( ) , h h u p of one-level method,which involves solving one large Navier-Stokes problem on a fine mesh with mesh size h. Hence,our method can save a large amount of computational time. Finally,some numerical tests confirm the theoretical expectations. Keywords—Navier-Stokes equations; equal-order pair; Newton iteration; Local Gauss integration; Two-level strategy ________________________________________________________________________________