Superconvergence of C0-Qk Finite Element Method for Elliptic Equations with Approximated Coefficients

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 interpolants 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.