A new second order nonconforming mixed finite element scheme for the stationary Stokes and Navier–Stokes equations

In this paper, a new stable nonconforming mixed finite element scheme with second order accuracy is proposed for the stationary Stokes and Navier–Stokes equations, in which, a new nonconforming rectangular element is taken for approximating space the velocity and the bilinear element for the pressure. The optimal error estimates for the approximation of both the velocity and the pressure in L2L2-norm are established, as well as one in a broken H1H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.