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Sharp A Posteriori Error Estimates for Optimal Control Governed by Parabolic Integro-Differential Equations

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Abstract

In this paper, we apply the finite element and backward Euler scheme for the space and time approximation of a constrained optimal control problem governed by a parabolic integro-differential equation on multi-meshes. We firstly establish the weak formulations for the control problem and then derive equivalent a posteriori error estimators with lower and upper bounds for both the state and the control approximation. These indicators are then used in our adaptive multi-meshes finite element schemes. Finally some numerical tests are presented to verify the effectiveness of the indicators.

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Author information

Authors and Affiliations

  1. School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, People’s Republic of China

    Wanfang Shen

  2. Shandong Provincial Key Laboratory of Computer Networks, Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan, 250004, People’s Republic of China

    Liang Ge

  3. Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

    Danping Yang

  4. KBS, University of Kent, Canterbury, CT2 7NF, UK

    Wenbin Liu

Authors
  1. Wanfang Shen
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  2. Liang Ge
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  3. Danping Yang
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  4. Wenbin Liu
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Corresponding author

Correspondence to Wenbin Liu.

Additional information

The research was partially supported by National Natural Foundation of China, Grants: 11326226, 11071080 and 11171113.

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Shen, W., Ge, L., Yang, D. et al. Sharp A Posteriori Error Estimates for Optimal Control Governed by Parabolic Integro-Differential Equations. J Sci Comput 65, 1–33 (2015). https://doi.org/10.1007/s10915-014-9957-3

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  • DOI: https://doi.org/10.1007/s10915-014-9957-3

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