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

Abstract

In this paper, the discretization of the stationary Stokes and Navier–Stokes equations in a two-dimensional domain by a nonconforming mixed finite element method is considered. The standard formulation of the Stokes and Navier–Stokes equations in the primitive variables is formed, which takes for approximating space the new nonconforming rectangular element for the velocity and the bilinear element for the pressure. The optimal error estimates for the approximations of both the velocity in broken H 1 -norm and the pressure in L 2 -norm are achieved. Numerical experiments are given which are consistent with our theoretical analysis.