Maximum–norm a posteriori error estimates for an optimal control problem

Abstract

We analyze a reliable and efficient max-norm a posteriori error estimator for a control-constrained, linear–quadratic optimal control problem. The estimator yields optimal experimental rates of convergence within an adaptive loop.

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Acknowledgements

E. Otárola was supported in part by CONICYT through FONDECYT project 11180193. A. J. Salgado was supported in part by NSF Grant DMS-1418784. R. Rankin was supported in part by Universidad de Chile through BASAL PFB03 CMM project. The authors would like to thank Alejandro Allendes.

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Otárola, E., Rankin, R. & Salgado, A.J. Maximum–norm a posteriori error estimates for an optimal control problem. Comput Optim Appl 73, 997–1017 (2019). https://doi.org/10.1007/s10589-019-00090-0

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Keywords

  • Linear–quadratic optimal control problem
  • Finite element methods
  • A posteriori error analysis
  • Maximum–norm

Mathematics Subject Classification

  • 49J20
  • 49M25
  • 65K10
  • 65N15
  • 65N30
  • 65N50
  • 65Y20