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Variational discretization for optimal control problems governed by parabolic equations

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Abstract

This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations. The state and co-state are approximated by Raviart-Thomas mixed finite element spaces, and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. A priori error estimates are derived for the state, the co-state, and the control. Some numerical examples are presented to confirm the theoretical investigations.

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Authors and Affiliations

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

    Yanping Chen & Tianliang Hou

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Nianyu Yi

Authors
  1. Yanping Chen
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  2. Tianliang Hou
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  3. Nianyu Yi
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Corresponding author

Correspondence to Yanping Chen.

Additional information

The first author and the second author are supported by the National Natural Science Foundation of China under Grant No. 11271145, Foundation for Talent Introduction of Guangdong Provincial University, Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20114407110009, and the Project of Department of Education of Guangdong Province under Grant No. 2012KJCX0036. The third author is partially supported by Hunan Education Department Key Project 10A117 and the National Natural Science Foundation of China under Grant Nos. 11126304 and 11201397.

This paper was recommended for publication by Editor YAN Ningning.

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Chen, Y., Hou, T. & Yi, N. Variational discretization for optimal control problems governed by parabolic equations. J Syst Sci Complex 26, 902–924 (2013). https://doi.org/10.1007/s11424-013-1166-x

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  • DOI: https://doi.org/10.1007/s11424-013-1166-x

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