Comparison of the Reduced-Basis and POD a-Posteriori Error Estimators for an Elliptic Linear-Quadratic Optimal Control Problem

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2011
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Tonn, Timo
Urban, Karsten
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Mathematical and Computer Modelling of Dynamical Systems. 2011, 17(4), pp. 355-369. ISSN 1387-3954. Available under: doi: 10.1080/13873954.2011.547678
Zusammenfassung

In this article, a linear-quadratic optimal control problem governed by the Helmholtz equation is considered. For the computation of suboptimal solutions, two different model reduction techniques are compared: the reduced-basis method (RBM) and proper orthogonal decomposition (POD). By an a-posteriori error estimator for the optimal control problem the accuracy of the suboptimal solutions is ensured. The efficiency of both model reduction approaches is illustrated by a numerical example for the stationary Helmholtz equation

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510 Mathematik
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optimal control, a-posteriori error estimate, proper orthogonal decomposition, reduced-basis method, Helmholtz equation
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ISO 690TONN, Timo, Karsten URBAN, Stefan VOLKWEIN, 2011. Comparison of the Reduced-Basis and POD a-Posteriori Error Estimators for an Elliptic Linear-Quadratic Optimal Control Problem. In: Mathematical and Computer Modelling of Dynamical Systems. 2011, 17(4), pp. 355-369. ISSN 1387-3954. Available under: doi: 10.1080/13873954.2011.547678
BibTex
@article{Tonn2011Compa-15354,
  year={2011},
  doi={10.1080/13873954.2011.547678},
  title={Comparison of the Reduced-Basis and POD a-Posteriori Error Estimators for an Elliptic Linear-Quadratic Optimal Control Problem},
  number={4},
  volume={17},
  issn={1387-3954},
  journal={Mathematical and Computer Modelling of Dynamical Systems},
  pages={355--369},
  author={Tonn, Timo and Urban, Karsten and Volkwein, Stefan}
}
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