A stabilized nonconfirming finite element method based on multiscale enrichment for the stationary Navier–Stokes equations

In the paper, we proposed a stabilized nonconforming finite element method for the stationary incompressible Navier–Stokes equations, which is a Petrov–Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. And we studied the stability of the method for P1-P0P1-P0 triangular element (Q1-P0Q1-P0 quadrilateral element) and obtained the optimal error estimates of the stabilized nonconforming finite element method for the stationary Navier–Stokes equations.