A new local stabilized nonconforming finite element method for solving stationary Navier–Stokes equations

In this paper we study a new local stabilized nonconforming finite element method based on two local Gauss integrals for solving the stationary Navier–Stokes equations. This nonconforming method utilizes the lowest equal-order pair of mixed finite elements (i.e., NCP1–P1). Error estimates of optimal order are obtained, and numerical results agreeing with these estimates are demonstrated. Numerical comparisons with other mixed finite element methods for solving the Navier–Stokes equations are also presented to show the better performance of the present method.