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Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems

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Abstract

In this paper, we investigate the discretization of general convex optimal control problem using the mixed finite element method. The state and co-state are discretized by the lowest order Raviart-Thomas element and the control is approximated by piecewise constant functions. We derive error estimates for both the control and the state approximation. Moreover, we present the superconvergence analysis for mixed finite element approximation of the optimal control problem. Finally, some numerical examples are given to demonstrate the practical side of the theoretical results about superconvergence.

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Authors and Affiliations

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

    Yanping Chen

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering; School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Yunqing Huang

  3. KBS & IMS, University of Kent, Canterbury, CT2 7NF, UK

    Wenbin Liu

  4. Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, 100080, China

    Ningning Yan

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  1. Yanping Chen
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  2. Yunqing Huang
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  3. Wenbin Liu
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  4. Ningning Yan
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Correspondence to Yanping Chen.

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Chen, Y., Huang, Y., Liu, W. et al. Error Estimates and Superconvergence of Mixed Finite Element Methods for Convex Optimal Control Problems. J Sci Comput 42, 382–403 (2010). https://doi.org/10.1007/s10915-009-9327-8

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  • DOI: https://doi.org/10.1007/s10915-009-9327-8

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