Interior error estimates for nonconforming finite element methods of the Stokes equations

Interior error estimates are derived for nonconforming stable mixed finite element discretizations of the stationary Stokes equations. As an application, interior convergences of difference quotients of the finite element solution are obtained for the derivatives of the exact solution when the mesh satisfies some translation invariant condition. For the linear element, it is proved that the average of the gradients of the finite element solution at the midpoint of two interior adjacent triangles approximates the gradient of the exact solution quadratically.