Convergence of adaptive finite elements for optimal control problems with control constraints

Abstract

We summarize our findings in the analysis of adaptive finite element methods for the efficient discretization of control constrained optimal control problems. We particularly focus on convergence of the adaptive method, i.e we show that the sequence of adaptively generated discrete solutions converges to the true solution. The result covers the variational discretization (Hinze) as well as control discretizations with piecewise discontinuous finite elements. Moreover, the presented theory can be applied to a large class of state equations, to boundary control and boundary observation.