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A Priori Error Analysis for the Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • S. May

    (University of Heidelberg, Institute of Applied Mathematics)

  • R. Rannacher

    (University of Heidelberg, Institute of Applied Mathematics)

  • B. Vexler

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

Abstract

This article presents recent results of an a priori error analysis for the finite element approximation of Dirichlet boundary control problems governed by elliptic partial differential equations. For a standard model problem error estimates are proven for the primal variable, the control, as well as the associated adjoint variable. These estimates are of optimal order with respect to the solution’s regularity to be expected on polygonal domains. The proofs rely on the Euler-Lagrange formulation of the optimal control problem and employ standard duality techniques and optimal-order L p error estimates for the finite element Ritz projection. These estimates improve corresponding results in the literature and are supported by computational experiments. The details are contained in [9].

Suggested Citation

  • S. May & R. Rannacher & B. Vexler, 2008. "A Priori Error Analysis for the Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 637-644, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_76
    DOI: 10.1007/978-3-540-69777-0_76
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