Geodesic
Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 771-800

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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.

DOI : 10.1051/cocv/2010025
Classification : 49M25, 35J60, 35B37, 65N30
Keywords: quasilinear elliptic equations, optimal control problems, finite element approximations, convergence of discretized controls 
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     author = {Casas, Eduardo and Tr\"oltzsch, Fredi},
     title = {Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {771--800},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {3},
     year = {2011},
     doi = {10.1051/cocv/2010025},
     mrnumber = {2826980},
     zbl = {1228.49033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010025/}
}
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Casas, Eduardo; Tröltzsch, Fredi. Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 771-800. doi: 10.1051/cocv/2010025

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