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Approximation of Sparse Controls in Semilinear Elliptic Equations

  • Eduardo Casas
  • Roland Herzog
  • Gerd Wachsmuth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

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.

Keywords

optimal control of partial differential equations sparse controls non-differentiable objective finite element discretization a priori error estimates semilinear equations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eduardo Casas
    • 1
  • Roland Herzog
    • 2
  • Gerd Wachsmuth
    • 2
  1. 1.Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de TelecomunicaciónUniversidad de CantabriaSantanderSpain
  2. 2.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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