  We consider a linear-quadratic elliptic optimal control problem with point
evaluations of the state variable in the cost functional. The state variable is
discretized by conforming linear finite elements. For control discretization,
three different approaches are considered. The main goal of the paper is to
significantly improve known a priori discretization error estimates for this
problem. We prove optimal error estimates for cellwise constant control
discretizations in two and three space dimensions. Further, in two space
dimensions, optimal error estimates for variational discretization and for the
post-processing approach are derived.
