A posteriori error estimates for convex boundary control problems. (English) Zbl 0988.49018

Summary: 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 \(C^{2}\) 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.


49M25 Discrete approximations in optimal control
49J20 Existence theories for optimal control problems involving partial differential equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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