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A Robust Preconditioner for Distributed Optimal Control for Stokes Flow with Control Constraints

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Numerical Mathematics and Advanced Applications 2011

Abstract

This work is devoted to the construction and analysis of robust solution techniques for the distributed optimal control problem for the Stokes equations with inequality constraints on the control. There the first order system of necessary and sufficient optimality conditions is nonlinear. A primal-dual active set method is applied in order to linearize the system. In every step a linear saddle point system has to be solved. For this system, we analyze a block-diagonal preconditioner that is robust with respect to the discretization parameter as well as the active set.

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Acknowledgements

The research was funded by the Austrian Science Fund (FWF): W1214-N15, project DK12.

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Authors and Affiliations

  1. Doctoral Program Computational Mathematics, Johannes Kepler University, Altenbergerstr. 69, A-4040, Linz, Austria

    M. Kollmann

  2. Institute of Computational Mathematics, Johannes Kepler University, Altenbergerstr. 69, A-4040, Linz, Austria

    W. Zulehner

Authors
  1. M. Kollmann
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  2. W. Zulehner
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Corresponding author

Correspondence to M. Kollmann .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Leicester, Leicester, LE!1 7RH, United Kingdom

    Andrea Cangiani

  2. , Department of Mathematics, University of Leicester, Leicester, LE1 7RL, United Kingdom

    Ruslan L. Davidchack

  3. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Emmanuil Georgoulis

  4. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Alexander N. Gorban

  5. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Jeremy Levesley

  6. , School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

    Michael V. Tretyakov

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Kollmann, M., Zulehner, W. (2013). A Robust Preconditioner for Distributed Optimal Control for Stokes Flow with Control Constraints. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_81

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