A mixedfinite element methodfor the solution of the Navier-Stokes equations is presented. The scheme uses discontinuousfinite elements that allow the utilization of upwind derivatives. This makes the scheme more stable and accelerates the convergence. Moreover the boundary layer is better consideredfor high Reynolds numbers. The existence of a solution and the convergence of the se heme are established. Results inside a square cavity far Re = 10000 far the recirculating jlow, the stream function and their second derivatives, viscous stress tensor and velocity vector are obtained. Between Re = 1000 and Re = 2000 a third secondary vortex appears nea, the upper right comer.