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


  • Eduardo Casas


  • Vili Dhamo



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

Suggested Citation

  • Eduardo Casas & Vili Dhamo, 2012. "Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations," Computational Optimization and Applications, Springer, vol. 52(3), pages 719-756, July.
  • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:719-756 DOI: 10.1007/s10589-011-9440-0

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    References listed on IDEAS

    1. de Klerk, E. & Elfadul, G.E.E. & den Hertog, D., 2006. "Optimization of Univariate Functions on Bounded Intervals by Interpolation and Semidefinite Programming," Discussion Paper 2006-26, Tilburg University, Center for Economic Research.
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