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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. 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.
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    5. 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.
    6. 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.
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