Numerische Mathematik

, Volume 122, Issue 4, pp 645-669

First online:

Approximation of sparse controls in semilinear equations by piecewise linear functions

  • Eduardo CasasAffiliated withDepartmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria
  • , Roland HerzogAffiliated withFaculty of Mathematics, Chemnitz University of Technology Email author 
  • , Gerd WachsmuthAffiliated withFaculty of Mathematics, Chemnitz University of Technology

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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