Reliable a posteriori error estimation for state-constrained optimal control

We derive a reliable a posteriori error estimator for a state‐constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non‐discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introduce an adaptation strategy for the regularisation parameter.