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Galerkin Spectral Approximation of Elliptic Optimal Control Problems with \(H^1\)-Norm State Constraint

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Abstract

In this paper, we study an elliptic optimal control problem with \(H^1\)-norm state constraint. The control problem is approximated by the Galerkin spectral method, which can provide high-order accuracy and fast convergence rate. The optimality conditions and a priori error estimates are presented. A reliable a posteriori error estimator is investigated, which is helpful for developing adaptive strategy in the spectral method. Some numerical tests confirm the error estimates and illustrate the performance of the indicator.

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Acknowledgments

The authors are grateful to the referees for their helpful and profound comments and advices.

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Authors and Affiliations

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

    Yanping Chen & Fenglin Huang

Authors
  1. Yanping Chen
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  2. Fenglin Huang
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Corresponding author

Correspondence to Yanping Chen.

Additional information

This work is supported by National Science Foundation of China (91430104, 11271145), Specialized Research Fund for the Doctoral Program of Higher Education (20114407110009), and the Scientific Research Foundation of Graduate School of South China Normal University (2014bsxm02).

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Chen, Y., Huang, F. Galerkin Spectral Approximation of Elliptic Optimal Control Problems with \(H^1\)-Norm State Constraint. J Sci Comput 67, 65–83 (2016). https://doi.org/10.1007/s10915-015-0071-y

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  • DOI: https://doi.org/10.1007/s10915-015-0071-y

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