A two-level variational multiscale method for incompressible flows based on two local Gauss integrations

In this article, a two-level variational multiscale method for incompressible flows based on two local Gauss integrations is presented. We solve the Navier-Stokes problem on a coarse mesh using finite element variational multiscale method based on two local Gauss integrations, then seek a fine grid solution by solving a linearized problem on a fine grid. In computation, we use the two local Gauss integrations to replace the projection operator without adding any variables. Stability analysis is performed, and error estimates of the method are derived. Finally, a series of numerical experiments are also given, which confirm the theoretical analysis and demonstrate the efficiency of the new method.