Stabilized Multiscale Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations

We consider a stabilized multiscale nonconforming finite element method for the two-dimensional stationary incompressible Navier-Stokes problem. This method is based on the enrichment of the standard polynomial space for the velocity component with multiscale function and the nonconforming lowest equal-order finite element pair. Stability and existence uniqueness of the numerical solution are established, optimal-order error estimates are also presented. Finally, some numerical results are presented to validate the performance of the proposed method.