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Approximation of Sparse Controls in Semilinear Elliptic Equations

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Book cover Large-Scale Scientific Computing (LSSC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

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Abstract

Semilinear elliptic optimal control problems involving the L 1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for three different discretizations for the control problem are given. These discretizations differ in the use of piecewise constant, piecewise linear and continuous or non-discretized controls, respectively. Numerical results and implementation details are provided.

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Author information

Authors and Affiliations

  1. Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Av. Los Castros s/n, 39005, Santander, Spain

    Eduardo Casas

  2. Faculty of Mathematics, Chemnitz University of Technology, Reichenhainer Strasse 41, 09126, Chemnitz, Germany

    Roland Herzog & Gerd Wachsmuth

Authors
  1. Eduardo Casas
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  2. Roland Herzog
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  3. Gerd Wachsmuth
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Block 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov  & Svetozar Margenov  & 

  2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, Building 321,, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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© 2012 Springer-Verlag Berlin Heidelberg

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Casas, E., Herzog, R., Wachsmuth, G. (2012). Approximation of Sparse Controls in Semilinear Elliptic Equations. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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