Discretization of nonlinear elliptic optimal control problems (Q1319504)

The authors consider a state-constrained optimal control problem for systems defined by semilinear elliptic partial differential equations. The relaxation theory, as presented by \textit{J. Warga} [Optimal control of differential and functional equations (1972; Zbl 0253.49001)], is applied to the study of the control problem. The main concern of the paper is the analysis of the numerical approximations. By using finite element methods, they discretize the control problem and prove that the limit points of the sequences of discrete optimal controls are solutions of the continuous relaxed problem.