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A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations

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Abstract

In this paper, we analyze the symmetric interior penalty Galerkin (SIPG) for distributed optimal control problems governed by unsteady convection diffusion equations with control constraint bounds. A priori error estimates are derived for the semi- and fully-discrete schemes by using piecewise linear functions. Numerical results are presented, which verify the theoretical results.

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Acknowledgements

The authors wish to thank the referees for their helpful suggestions and comments. This research was supported by the Middle East Technical University Scientific Research Fund (Project: BAP-07-05-2012-102).

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  1. Hamdullah Yücel

    Present address: Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

Authors and Affiliations

  1. Department of Mathematics & Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Tuğba Akman, Hamdullah Yücel & Bülent Karasözen

Authors
  1. Tuğba Akman
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  2. Hamdullah Yücel
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Correspondence to Hamdullah Yücel.

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Akman, T., Yücel, H. & Karasözen, B. A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations. Comput Optim Appl 57, 703–729 (2014). https://doi.org/10.1007/s10589-013-9601-4

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