Reduced basis a posteriori error bounds for parametrized linear-quadratic elliptic optimal control problems |
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| Authors: | Martin A. Grepl Mark Kärcher |
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| Affiliation: | 1. Institut für Geometrie und Praktische Mathematik (IGPM), RWTH Aachen University, 52056 Aachen, Germany;2. Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, 52056 Aachen, Germany |
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| Abstract: | We employ the reduced basis method as a surrogate model for the solution of optimal control problems governed by parametrized partial differential equations (PDEs) and develop rigorous a posteriori error bounds for the error in the optimal control and the associated error in the cost functional. The proposed bounds can be efficiently evaluated in an offline–online computational procedure. We present numerical results that confirm the validity of our approach. |
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