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A Posteriori Error Estimates for Semilinear Boundary Control Problems

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Domain Decomposition Methods in Science and Engineering XIX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 78))

Abstract

In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numerical methods for these problems. The approximation of optimal control by piecewise constant functions is well investigated by [7, 8]. The discretization for semilinear elliptic optimal control problems is discussed in [2]. Systematic introductions of the finite element method for optimal control problems can be found in [10].

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Acknowledgments

The authors express their thanks to the referees for their helpful suggestions, which led to improvements of the presentation.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, P.R.China

    Yanping Chen

  2. College of Mathematics and Computer Sciences, Chongqing Three Gorges University, Chongqing, 404000, P.R.China

    Zuliang Lu

Authors
  1. Yanping Chen
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  2. Zuliang Lu
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Corresponding author

Correspondence to Yanping Chen .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Xiangtan University, Xiangtan, 411105, China, People's Republic

    Yunqing Huang

  2. FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Berlin, Germany

    Ralf Kornhuber

  3. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Olof Widlund

  4. Eberly College of Science, Dept. Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Jinchao Xu

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© 2011 Springer-Verlag Berlin Heidelberg

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Chen, Y., Lu, Z. (2011). A Posteriori Error Estimates for Semilinear Boundary Control Problems. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_53

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