  We present a priori and superconvergence error estimates of mixed finite
element methods for the pseudostress-velocity formulation of the Oseen
equation. In particular, we derive superconvergence estimates for the velocity
and a priori error estimates under unstructured grids, and obtain
superconvergence results for the pseudostress under certain structured grids. A
variety of numerical experiments validate the theoretical results and
illustrate the effectiveness of the superconvergent recovery-based adaptive
mesh refinement. It is also numerically shown that the proposed postprocessing
yields apparent superconvergence in a benchmark problem for the incompressible
Navier--Stokes equation.
