Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations

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URI: http://hdl.handle.net/10902/1617
ISSN: 1262-3377
ISSN: 1292-8119
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Autoría
Casas Rentería, EduardoAutoridad Unican; Tröltzsch, FrediAutoridad Unican
Fecha
2011-07
Derechos
© EDP Sciences, SMAI, 2010. The original publication is available at www.esaim-cocv.org
Publicado en
ESAIM: Control, Optimisation and Calculus of Variations, 2011, 17(3), 771-800
Editorial
EDP Sciences
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Palabras clave
Quasilinear elliptic equations
Optimal control problems
Finite element approximations
Convergence of discretized controls
Resumen/Abstract
In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the uniqueness of a solution for the discrete equation is an open problem.
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