Abstract
A block finite element difference scheme is derived from the next to the lowest order Raviart-Thomas mixed quadrilateral finite element method by using some numerical quadratures element-wise. This finite difference scheme is much simpler than the mixed finite element method itself with the same order of accuracy. Superconvergence error estimates of order $O(h^3 )$ for both the pressure and the Darcy velocity are established, even for certain discontinuous coefficients. Numerical experiments are presented to confirm the analysis at the end of this paper.
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