  In this paper, an abstract framework for the error analysis of discontinuous
finite element method is developed for the distributed and Neumann boundary
control problems governed by the stationary Stokes equation with control
constraints. {\it A~priori} error estimates of optimal order are derived for
velocity and pressure in the energy norm and the $L^2$-norm, respectively.
Moreover, a reliable and efficient {\it a~posteriori} error estimator is
derived. The results are applicable to a variety of problems just under the
minimal regularity possessed by the well-posedness of the problem. In
particular, we consider the abstract results with suitable stable pairs of
velocity and pressure spaces like as the lowest-order Crouzeix-Raviart finite
element and piecewise constant spaces, piecewise linear and constant finite
element spaces. The theoretical results are illustrated by the numerical
experiments.
