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A Priori Error Analysis for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • D. Meidner

    (Technische Universität München, Fakultät für Mathematik, Lehrstuhl für Mathematische Optimierung)

  • B. Vexler

    (Technische Universität München, Fakultät für Mathematik, Lehrstuhl für Mathematische Optimierung)

Abstract

In this article we discuss a priori error estimates for Galerkin finite element discretizations of optimal control problems governed by linear parabolic equations and subject to inequality control constraints. The space discretization of the state variable is done using usual conforming finite elements, whereas the time discretization is based on discontinuous Galerkin methods. For different types of control discretizations we provide error estimates of optimal order with respect to both space and time discretization parameters taking into account the spatial and the temporal regularity of the optimal solution. For the treatment of the control discretization we discuss different approaches extending techniques known from the elliptic case. For detailed proofs and numerical results we refer to [18, 19].

Suggested Citation

  • D. Meidner & B. Vexler, 2008. "A Priori Error Analysis for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 645-652, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_77
    DOI: 10.1007/978-3-540-69777-0_77
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