Interior Error Estimates for Nonconforming Finite Element Methods of the Stokes Equations (Journal of Computational Mathematics, 1999)
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 forthe derivatives of the exact solution when the mesh satisfied some translation invariant condition. For the linear element, it is proved that the average of thegradients of the finite element solution at the midpoint of two interior adjacenttriangles approximates the gradient of the exact solution quadratically.