An Upwind Nonlinear Galerkin Finite Element Method For The Stationary Navier-Stokes Equations

In order to solve the Navier-Stokes equations in the case of the high Reynolds number, we combine the nonlinear Galerkin method with the upwind finite element method and an upwind nonlinear Galerkin method is presented for the stationary incompressible Navier-Stokes equations in two dimensional domain. Meanwhile its convergence is given. The upwind nonlinear Galerkin finite element method consists in solving a linear subproblem on a coarse grid incremental finite element space and solving a linear subproblem on a fine grid incremental finite element space, which can salve a large amount of computational time and judge convergence easily comparing with the upwind finite element method.