Numerische Mathematik

, Volume 122, Issue 4, pp 645–669

Approximation of sparse controls in semilinear equations by piecewise linear functions


  • Eduardo Casas
    • Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de TelecomunicaciónUniversidad de Cantabria
    • Faculty of MathematicsChemnitz University of Technology
  • Gerd Wachsmuth
    • Faculty of MathematicsChemnitz University of Technology

DOI: 10.1007/s00211-012-0475-7

Cite this article as:
Casas, E., Herzog, R. & Wachsmuth, G. Numer. Math. (2012) 122: 645. doi:10.1007/s00211-012-0475-7


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


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© Springer-Verlag 2012