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L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

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Abstract

This paper investigates L ∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. The authors derive L ∞-estimates for the mixed finite element approximation of nonlinear optimal control problems. Finally, the numerical examples are given.

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Authors and Affiliations

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

    Yanping Chen

  2. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, China

    Zuliang Lu

  3. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, China

    Zuliang Lu

Authors
  1. Yanping Chen
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  2. Zuliang Lu
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Correspondence to Yanping Chen.

Additional information

This work is supported by the Foundation for Talent Introduction of Guangdong Provincial University, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2008), National Science Foundation of China under Grant No. 10971074, and China Postdoctoral Science Foundation under Grant No. 2011M500968.

This paper was recommended for publication by Editor Ningning YAN.

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Chen, Y., Lu, Z. L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems. J Syst Sci Complex 25, 105–120 (2012). https://doi.org/10.1007/s11424-011-9215-9

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  • DOI: https://doi.org/10.1007/s11424-011-9215-9

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