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Mimetic Discretizations of Elliptic Control Problems

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Abstract

We investigate the performance of the Mimetic Finite Difference (MFD) method for the approximation of a constraint optimal control problem governed by an elliptic operator. Low-order and high-order mimetic discretizations are considered and a priori error estimates are derived, in a suitable discrete norm, for both the control and the state variables. A wide class of numerical experiments performed on a set of examples selected from the literature assesses the robustness of the MFD method and confirms the convergence analysis.

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Acknowledgements

We would like to thank the anonymous Referee for his/her valuable suggestions. This work was partially supported by Azione Integrata Italia-Spagna through the project IT097ABB10.

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Authors and Affiliations

  1. MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Paola F. Antonietti, Nadia Bigoni & Marco Verani

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  1. Paola F. Antonietti
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  2. Nadia Bigoni
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  3. Marco Verani
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Correspondence to Nadia Bigoni.

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Antonietti, P.F., Bigoni, N. & Verani, M. Mimetic Discretizations of Elliptic Control Problems. J Sci Comput 56, 14–27 (2013). https://doi.org/10.1007/s10915-012-9659-7

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  • DOI: https://doi.org/10.1007/s10915-012-9659-7

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