Numerische Mathematik

, Volume 122, Issue 4, pp 645–669

Approximation of sparse controls in semilinear equations by piecewise linear functions

Article

Abstract

Semilinear elliptic optimal control problems involving the \(L^1\) norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.

Mathematics Subject Classification

35J61 49K20 49M25 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de TelecomunicaciónUniversidad de Cantabria SantanderSpain
  2. 2.Faculty of MathematicsChemnitz University of Technology ChemnitzGermany

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