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Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems

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Abstract

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, error estimates are established and some numerical experiments, which confirm the theoretical results, are performed.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39071, Santander, Spain

    Eduardo Casas

  2. Departamento de Matemáticas, E.P.S.I. de Gijón, Universidad de Oviedo, Campus de Viesques, 33203, Gijón, Spain

    Mariano Mateos

  3. Institut für Mathematik, Technische Universität Berlin, 10623, Berlin, Germany

    Fredi TrÖltzsch

Authors
  1. Eduardo Casas
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  2. Mariano Mateos
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  3. Fredi TrÖltzsch
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Correspondence to Eduardo Casas.

Additional information

The first two authors were supported by Ministerio de Ciencia y Tecnología (Spain). The second author was also supported by the DFG research center “Mathematics for key technologies” (FZT86) in Berlin.

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Casas, E., Mateos, M. & TrÖltzsch, F. Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems. Comput Optim Applic 31, 193–219 (2005). https://doi.org/10.1007/s10589-005-2180-2

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  • DOI: https://doi.org/10.1007/s10589-005-2180-2

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