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A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems

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Abstract

In this paper, we derive a posteriori error estimates of recovery type, and present the superconvergence analysis for the finite element approximation of distributed convex optimal control problems. We provide a posteriori error estimates of recovery type for both the control and the state approximation, which are generally equivalent. Under some stronger assumptions, they are further shown to be asymptotically exact. Such estimates, which are apparently not available in the literature, can be used to construct adaptive finite element approximation schemes and as a reliability bound for the control problems. Numerical results demonstrating our theoretical results are also presented in this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Ruo Li

  2. KBS & Institute of Mathematics and Statistics, The University of Kent, Canterbury, CT2 7NF, England

    Wenbin Liu

  3. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Ningning Yan

Authors
  1. Ruo Li
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  2. Wenbin Liu
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  3. Ningning Yan
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Correspondence to Ruo Li.

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Li, R., Liu, W. & Yan, N. A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems. J Sci Comput 33, 155–182 (2007). https://doi.org/10.1007/s10915-007-9147-7

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  • DOI: https://doi.org/10.1007/s10915-007-9147-7

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