Finite element approximation and iterative method solution of elliptic control problem with constraints to gradient of state

An optimal control problem with distributed control in the right-hand side of Poisson equation is considered. Pointwise constraints on the gradient of state and control are imposed in this problem. The convergence of nite element approxima-tion for this problem is proved. Discrete saddle point problem is constructed and preconditioned Uzawa-type iterative algorithm for its solution is investigated