In the framework of the mixed finite element approximation of a second- order elliptic equation studied by P. A. Raviart and J. M. Thomas and much more others, this paper proposes some interesting improvements valid on rectangular domain when using the lowest-order rectangular element:
i) superconvergence results on the approximation along the Gauss lines for the vector field;
ii) a procedure of postprocessed extrapolation for the scalar field;
iii) procedures of pure Richardson extrapolation for both the vector and the scalar fields.
All these results are based on asymptotic expansions and they all yield approximations of higher order to the original problem.