Approximation of sparse controls in semilinear elliptic equations

Authors:
Eduardo Casas;Roland Herzog;Gerd Wachsmuth
Affiliations:
Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Santander, Spain;Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany;Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
Venue:
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Year:
2011

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Abstract

Semilinear elliptic optimal control problems involving the L1 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.