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Numerical analysis of POD A-posteriori error estimation for optimal control

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2013

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http://nbn-resolving.de/urn:nbn:de:bsz:352-264571
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https://doi.org/10.1007/978-3-0348-0631-2_8
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BREDIES, Kristian, ed., Christian CLASON, ed., Karl KUNISCH, ed., Gregory VON WINCKEL, ed.. Control and Optimization with PDE Constraints. Basel: Springer Basel, 2013, pp. 137-158. ISSN 0373-3149. ISBN 978-3-0348-0630-5. Available under: doi: 10.1007/978-3-0348-0631-2_8

Zusammenfassung

In this paper a linear-quadratic optimal control problem governed by a parabolic equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. In this paper the authors focus on testing the a-posteriori estimate’s validity by means of numerical examples. An intensive study of the consequences of certain choices that can be made within the POD basis determination process is carried out and the findings are discussed.

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510 Mathematik

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ISO 690STUDINGER, Alina, Stefan VOLKWEIN, 2013. Numerical analysis of POD A-posteriori error estimation for optimal control. In: BREDIES, Kristian, ed., Christian CLASON, ed., Karl KUNISCH, ed., Gregory VON WINCKEL, ed.. Control and Optimization with PDE Constraints. Basel: Springer Basel, 2013, pp. 137-158. ISSN 0373-3149. ISBN 978-3-0348-0630-5. Available under: doi: 10.1007/978-3-0348-0631-2_8
BibTex
@incollection{Studinger2013Numer-26457,
  year={2013},
  doi={10.1007/978-3-0348-0631-2_8},
  title={Numerical analysis of POD A-posteriori error estimation for optimal control},
  isbn={978-3-0348-0630-5},
  publisher={Springer Basel},
  address={Basel},
  booktitle={Control and Optimization with PDE Constraints},
  pages={137--158},
  editor={Bredies, Kristian and Clason, Christian and Kunisch, Karl and von Winckel, Gregory},
  author={Studinger, Alina and Volkwein, Stefan}
}
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