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Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem

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Abstract

We study the numerical approximation of distributed nonlinear optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Our main result are error estimates for optimal controls in the maximum norm. Characterization results are stated for optimal and discretized optimal control. Moreover, the uniform convergence of discretized controls to optimal controls is proven under natural assumptions.

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, D-09107, Chemnitz, Germany

    Nadir Arada

  2. Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, 39005, Santander, Spain

    Eduardo Casas

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

    Fredi Tröltzsch

Authors
  1. Nadir Arada
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  2. Eduardo Casas
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  3. Fredi Tröltzsch
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Arada, N., Casas, E. & Tröltzsch, F. Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem. Computational Optimization and Applications 23, 201–229 (2002). https://doi.org/10.1023/A:1020576801966

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