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Finite element approximation for a class of parameter estimation problems

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Abstract

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations, where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. The authors derive some a priori error estimates for both the control and state approximations. Finally, the numerical experiments verify the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, China

    Yanzhen Chang

  2. Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200062, China

    Danping Yang

Authors
  1. Yanzhen Chang
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  2. Danping Yang
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Corresponding author

Correspondence to Yanzhen Chang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11101025, 11071080, 11171113, the Fundamental Research Funds for the Central Universities and the Youth Foundation of Tianyuan Mathematics, the National Natural Science Foundation of China under Grant No. 11126279.

This paper was recommended for publication by Editor HONG Yiguang.

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Chang, Y., Yang, D. Finite element approximation for a class of parameter estimation problems. J Syst Sci Complex 27, 866–882 (2014). https://doi.org/10.1007/s11424-014-1218-x

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  • DOI: https://doi.org/10.1007/s11424-014-1218-x

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