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Numerical Analysis of a Control and State Constrained Elliptic Control Problem with Piecewise Constant Control Approximations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • K. Deckelnick

    (Otto-von-Guericke-Universität Magdeburg, Institut für Analysis und Numerik)

  • M. Hinze

    (Universität Hamburg, Schwerpunkt Optimierung und Approximation)

Abstract

We consider an elliptic optimal control problem with control and pointwise state constraints. The cost functional is approximated by a sequence of functionals which are obtained by discretizing the state equation with the help of linear finite elements and enforcing the state constraints in the nodes of the triangulation. Controls are discretized piecewise constant on every simplex of the triangulation. Error bounds for control and state are obtained both in two and three space dimensions.

Suggested Citation

  • K. Deckelnick & M. Hinze, 2008. "Numerical Analysis of a Control and State Constrained Elliptic Control Problem with Piecewise Constant Control Approximations," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 597-604, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_71
    DOI: 10.1007/978-3-540-69777-0_71
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