Uniform convergence of the FEM. Applications tostate constrained control problems

Abstract

In this paper we focus the numerical discretization of a stateconstrained control problem governed by a semilinear elliptic equation. Dis-tributed and boundary controls are considered. We study the convergence ofthe discrete optimal controls to the continuous optimal controls in the weakand strong topologies. Previous to this analysis we obtain some results of con-vergence in theL∞norm of the approximations of the state equation by finiteelements, which is essential to deal with the pointwise state constraints