A certified reduced basis method for parametrized elliptic optimal control problems

In this paper, we employ the reduced basis method as a surrogate model for the solu- tion of linear-quadratic optimal control problems governed by parametrized elliptic partial dierential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the as- sumption of ane parameter dependence, the reduced order optimal control problem and the proposed bounds can be eciently evaluated in an oine-online computational procedure. Numerical results are presented to conrm the validity of our approach.

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