Superconvergent Recovery of Raviart-Thomas Mixed Finite Elements on Triangular Grids

For the second lowest order Raviart-Thomas mixed method, we prove that the canonical interpolant and finite element solution for the vector variable in elliptic problems are superclose in the H(mml:mspace width="0.166667em"mml:mspacedivmml:mspace width="0.166667em"mml:mspace)-norm on mildly structured meshes, where most pairs of adjacent triangles form approximate parallelograms. We then develop a family of postprocessing operators for Raviart-Thomas mixed elements on triangular grids by using the idea of local least squares fittings. Super-approximation property of the postprocessing operators for the lowest and second lowest order Raviart-Thomas elements is proved under mild conditions. Combining the supercloseness and super-approximation results, we prove that the postprocessed solution superconverges to the exact solution in the L2-norm on mildly structured meshes.