Approximation of sparse controls in semilinear equations by piecewise linear functions

Semilinear elliptic optimal control problems involving the 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 discret...

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Bibliographic Details
Published inNumerische Mathematik Vol. 122; no. 4; pp. 645 - 669
Main Authors Casas, Eduardo, Herzog, Roland, Wachsmuth, Gerd
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.12.2012
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
35J61
49M25
49K20
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ISSN0029-599X
0945-3245
DOI10.1007/s00211-012-0475-7

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Summary:Semilinear elliptic optimal control problems involving the 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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-012-0475-7