  The purpose of this work is the design and analysis of a reliable and
efficient a posteriori error estimator for the so-called pointwise tracking
optimal control problem. This linear-quadratic optimal control problem entails
the minimization of a cost functional that involves point evaluations of the
state, thus leading to an adjoint problem with Dirac measures on the right hand
side; control constraints are also considered. The proposed error estimator
relies on a posteriori error estimates in the maximum norm for the state and in
Muckenhoupt weighted Sobolev spaces for the adjoint state. We present an
analysis that is valid for two and three-dimensional domains. We conclude by
presenting several numerical experiments which reveal the competitive
performance of adaptive methods based on the devised error estimator.
