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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

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

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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    Cited by:

    1. Mengya Su & Liuqing Xie & Zhiyue Zhang, 2022. "Numerical Analysis of Fourier Finite Volume Element Method for Dirichlet Boundary Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domains," Mathematics, MDPI, vol. 10(24), pages 1-26, December.

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