  We prove that the superconvergence of $C^0$-$Q^k$ finite element method at
the Gauss Lobatto quadrature points still holds if variable coefficients in an
elliptic problem are replaced by their piecewise $Q^k$ Lagrange interpolant at
the Gauss Lobatto points in each rectangular cell. In particular, a fourth
order finite difference type scheme can be constructed using $C^0$-$Q^2$ finite
element method with $Q^2$ approximated coefficients.
