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Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

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  • Hamdullah Yücel
  • Peter Benner

Abstract

We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau–Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented to illustrate the effectiveness of the adaptivity for both regularization techniques. Copyright Springer Science+Business Media New York 2015

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  • Hamdullah Yücel & Peter Benner, 2015. "Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations," Computational Optimization and Applications, Springer, vol. 62(1), pages 291-321, September.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:1:p:291-321
    DOI: 10.1007/s10589-014-9691-7
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    References listed on IDEAS

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    1. M. Hinze & C. Meyer, 2010. "Variational discretization of Lavrentiev-regularized state constrained elliptic optimal control problems," Computational Optimization and Applications, Springer, vol. 46(3), pages 487-510, July.
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    3. Michael Hinze & Anton Schiela, 2011. "Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment," Computational Optimization and Applications, Springer, vol. 48(3), pages 581-600, April.
    4. K. Krumbiegel & A. Rösch, 2009. "A virtual control concept for state constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 43(2), pages 213-233, June.
    5. Olaf Benedix & Boris Vexler, 2009. "A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints," Computational Optimization and Applications, Springer, vol. 44(1), pages 3-25, October.
    6. W. Wollner, 2010. "A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints," Computational Optimization and Applications, Springer, vol. 47(1), pages 133-159, September.
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    Cited by:

    1. Hailing Wang & Changjun Yu & Yongcun Song, 2024. "An Augmented Lagrangian Method for State Constrained Linear Parabolic Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 196-226, October.

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