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Finite and Boundary Element Energy Approximations of Dirichlet Control Problems

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • Günther Of

    (Graz University of Technology, Institute of Computational Mathematics)

  • Thanh Xuan Phan

    (Graz University of Technology, Institute of Computational Mathematics)

  • Olaf Steinbach

    (Graz University of Technology, Institute of Computational Mathematics)

Abstract

We study a Dirichlet boundary control problem of the Poisson equation where the Dirichlet control is considered in the energy space H 1∕2(Γ). Both, finite and boundary element approximations of the minimal solution are presented. We state the unique solvability of both approaches, as well as the stability and error estimates. The numerical example is in good agreement with the theoretical results.

Suggested Citation

  • Günther Of & Thanh Xuan Phan & Olaf Steinbach, 2012. "Finite and Boundary Element Energy Approximations of Dirichlet Control Problems," Springer Books, in: Hans Georg Bock & Xuan Phu Hoang & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes, edition 127, pages 219-231, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25707-0_18
    DOI: 10.1007/978-3-642-25707-0_18
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