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Numerical analysis of some optimal control problemsgoverned by a class of quasilinear elliptic equations*

Published online by Cambridge University Press:  06 August 2010

Eduardo Casas  and
Fredi Tröltzsch
Eduardo Casas
Affiliation:
Dpto. de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain. eduardo.casas@unican.es
Fredi Tröltzsch
Affiliation:
Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany. troeltzsch@math.tu-berlin.de
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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.

Keywords

Quasilinear elliptic equationsoptimal control problemsfinite element approximationsconvergence of discretized controls
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 3 , July 2011 , pp. 771 - 800
Copyright
© EDP Sciences, SMAI, 2010

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References

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