Iterative finite element variational multiscale method for the incompressible Navier-Stokes equations

Three iterative finite element variational multiscale methods are proposed and applied to the numerical simulation of the Navier-Stokes equations. The main idea of these methods is to combine the finite element variational multiscale method based on two local Gauss integrations with three different iterative schemes. The existence and uniqueness of approximate solutions of these iterative finite element variational multiscale methods are proved firstly, and then the convergence and error estimates of them are deduced. Finally, some numerical examples are given to support the theoretical analysis. The numerical results show that the iterative finite element variational multiscale method has a wider range of Reynolds numbers than standard Galerkin iterative finite element method, and the Oseen iterative scheme is much more efficient than the other two under high Reynolds numbers.