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Error estimates for the discretization of elliptic control problems with pointwise control and state constraints

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Abstract

A family of elliptic optimal control problems with pointwise constraints on control and state is considered. We are interested in approximation of the optimal solution by a finite element discretization of the involved partial differential equations. The discretization error for a problem with mixed state constraints is estimated in the semidiscrete case and in the fully discrete scheme with the convergence of order h|ln h| and h 1/2, respectively. However, considering the unregularized continuous problem and the discrete regularized version, and choosing suitable relation between the regularization parameter and the mesh size, i.e., ε∼h 2, a convergence order arbitrary close to 1, i.e., h 1−β is obtained. Therefore, we benefit from tuning the involved parameters.

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  1. Fachbereich Mathematik, University Duisburg-Essen, Forsthausweg 2, 47048, Duisburg, Germany

    S. Cherednichenko & A. Rösch

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  1. S. Cherednichenko
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  2. A. Rösch
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Correspondence to A. Rösch.

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Cherednichenko, S., Rösch, A. Error estimates for the discretization of elliptic control problems with pointwise control and state constraints. Comput Optim Appl 44, 27–55 (2009). https://doi.org/10.1007/s10589-008-9186-5

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  • DOI: https://doi.org/10.1007/s10589-008-9186-5

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