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Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations

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  • Eduardo Casas

    ()

  • Vili Dhamo

    ()

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    Abstract

    We study the numerical approximation of Neumann boundary optimal control problems governed by a class of quasilinear elliptic equations. The coefficients of the main part of the operator depend on the state function, as a consequence the state equation is not monotone. We prove that strict local minima of the control problem can be approximated uniformly by local minima of discrete control problems and we also get an estimate of the rate of this convergence. One of the main issues in this study is the error analysis of the discretization of the state and adjoint state equations. Some difficulties arise due to the lack of uniqueness of solution of the discrete equations. The theoretical results are illustrated by numerical tests. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-011-9440-0
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 52 (2012)
    Issue (Month): 3 (July)
    Pages: 719-756

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    Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:719-756

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Neumann boundary control; Quasilinear elliptic equation; Numerical approximation; Error estimates;

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