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Space-Time Discontinuous Galerkin Methods for Optimal Control Problems Governed by Time Dependent Diffusion-Convection-Reaction Equations

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Multiple Shooting and Time Domain Decomposition Methods

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 9))

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Abstract

In this paper, space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by discontinuous Galerkin method with piecewise constant and linear polynomials, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We present some numerical results in order to evaluate the performance of the method.

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Acknowledgements

The authors thank to Konstantinos Chrysafinos for his explanations regarding error estimates and references. This research was supported by the Middle East Technical University Research Fund Project (BAP-07-05-2012-102).

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Authors and Affiliations

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

    Tuğba Akman & Bülent Karasözen

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  1. Tuğba Akman
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  2. Bülent Karasözen
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Correspondence to Tuğba Akman .

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Editors and Affiliations

  1. Heidelberg University, Institute for Applied Mathematics, Heidelberg, Germany

    Thomas Carraro

  2. Heidelberg University, Institute for Applied Mathematics, Heidelberg, Germany

    Michael Geiger

  3. Heidelberg University, Interdisciplinary Center for Scientific Computing, Heidelberg, Germany

    Stefan Körkel

  4. Heidelberg University, Institute for Applied Mathematics, Heidelberg, Germany

    Rolf Rannacher

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Akman, T., Karasözen, B. (2015). Space-Time Discontinuous Galerkin Methods for Optimal Control Problems Governed by Time Dependent Diffusion-Convection-Reaction Equations. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds) Multiple Shooting and Time Domain Decomposition Methods. Contributions in Mathematical and Computational Sciences, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-23321-5_9

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