Adaptive Finite Element Method for an Elliptic Optimal Control Problem with Integral State Constraints

In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different sets of constraints, namely (i) integral state constraint and integral control constraint; (ii) integral state constraint and pointwise control constraints. In the analysis, we have taken the approach of reducing the state-control constrained minimization problem into a state minimization problem obtained by eliminating the control variable. The reliability and efficiency of a posteriori error estimator are discussed. Numerical results are reported to illustrate the behavior of the error estimator.