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A posteriori error estimates for distributed convex optimal control problems. (English) Zbl 1008.49024
The authors consider the following distributed convex optimal control problem $\min_{u\in C} \{g(y)+ h(u)\},\quad -\text{div}(A\nabla y)= f+ Bu\quad\text{in }\Omega,\quad y|_{\partial\Omega}= 0.$ For this problem, an a posteriori error analysis for finite element approximation is given. Explicit estimates are presented for some model problems which appear in real-life applications.

##### MSC:
 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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