We present an a posteriori error analysis of adaptive finite
element approximations of distributed control problems for second
order elliptic boundary value problems under bound constraints on
the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element
residuals. Since we do not assume any regularity of the data of
the problem, the error analysis further invokes data oscillations.
We prove reliability and efficiency of the error estimator and
provide a bulk criterion for mesh refinement that also takes into
account data oscillations and is realized by a greedy algorithm. A
detailed documentation of numerical results for selected test
problems illustrates the convergence of the adaptive finite
element method.