Certain finite difference methods on rectangular grids for second order elliptic equations are known to yield superconvergent flux approximations. A class of related finite difference methods have recently been defined for triangular meshes by applying special quadrature rules to an extended version of a mixed finite element method [1]; the flux vector fields from these methods are not superconvergent. This report presents empirical evidence indicating that a simple local postprocessing technique recovers higher order accurate vector velocities at element centers on many meshes of triangular elements, with approximately second order accuracy on three lines meshes.