  In this paper, error estimates are presented for a certain class of optimal
control problems with elliptic PDE-constraints. It is assumed that in the cost
functional the state is measured in terms of the energy norm generated by the
state equation. The functional a posteriori error estimates developed by Repin
in late 90's are applied to estimate the cost function value from both sides
without requiring the exact solution of the state equation. Moreover, a lower
bound for the minimal cost functional value is derived. A meaningful error
quantity coinciding with the gap between the cost functional values of an
arbitrary admissible control and the optimal control is introduced. This error
quantity can be estimated from both sides using the estimates for the cost
functional value. The theoretical results are confirmed by numerical tests.
