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Numerical approximation of elliptic control problems with finitely many pointwise constraints

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Abstract

We study the numerical approximation of elliptic control problems with finitely many pointwise state constraints and control bounds. Results for the continuous problem are collected and a complete study of the discrete problems is carried out, including, existence of solutions, optimality conditions, convergence to solutions of the continuous problem and error estimates. A numerical example is provided.

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Authors and Affiliations

  1. Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005, Santander, Spain

    Eduardo Casas

  2. Departmento de Matemáticas, E.P.I. Gijón, Universidad de Oviedo, Campus de Gijón, 33203, Gijón, Spain

    Mariano Mateos

Authors
  1. Eduardo Casas
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  2. Mariano Mateos
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Correspondence to Eduardo Casas.

Additional information

The authors were partially supported by the Spanish Ministerio de Ciencia e Innovación under projects MTM2008-04206 and “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider Ingenio 2010).

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Casas, E., Mateos, M. Numerical approximation of elliptic control problems with finitely many pointwise constraints. Comput Optim Appl 51, 1319–1343 (2012). https://doi.org/10.1007/s10589-011-9394-2

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  • DOI: https://doi.org/10.1007/s10589-011-9394-2

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