A Posteriori Error Estimates for Convex Boundary Control Problems

In this paper, we present an a posteriori error analysis for the finite element approximation of convex optimal Neumann boundary control problems. We derive a posteriori error estimates for both the state and the control approximation, first on polygonal domains and then on Lipschitz piecewise C2 domains. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for the control problems. Explicit estimates are shown for some model problems that frequently appear in applications.