A Petrov-Galerkin Least Squares Two Level Finite Element Method For The Stationary Navier-Stokes Equations

In this paper, a Petrov-Galerkin least squares two level finite element method is presented and analyzed for the stationary Navier-Stokes equations. The advantage of this method is that we only need solve a small nonlinear problem on a coarse mesh finite element space X_ H, and solve a linear problem on a fine mesh finite element space X_h( h << H). The finite element mathematic theory analysis was given in the cases of solution is exist, unique and branches of nonsingular solutions of N-S equations. We proved if is chosen, the convergence order of the method is the same as those of the paper [6] and [14]. And this method can save a lot of computation time.