  In this paper error analysis for finite element discretizations of Dirichlet
boundary control problems is developed. For the first time, optimal
discretization error estimates are established in the case of three dimensional
polyhedral and convex domains. The convergence rates solely depend on the size
of largest interior edge angle. These results are comparable to those for the
two dimensional case. However, the approaches from the two dimensional setting
are not directly extendable such that new techniques have to be used. The
theoretical results are confirmed by numerical experiments.
