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

Eduardo Casas; Fredi Tröltzsch

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 771-800
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Casas, Eduardo, and Tröltzsch, Fredi. "Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 771-800. <http://eudml.org/doc/272858>.

@article{Casas2011,
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.},
author = {Casas, Eduardo, Tröltzsch, Fredi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {quasilinear elliptic equations; optimal control problems; finite element approximations; convergence of discretized controls},
language = {eng},
number = {3},
pages = {771-800},
publisher = {EDP-Sciences},
title = {Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations},
url = {http://eudml.org/doc/272858},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Casas, Eduardo
AU - Tröltzsch, Fredi
TI - Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 3
SP - 771
EP - 800
AB - 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.
LA - eng
KW - quasilinear elliptic equations; optimal control problems; finite element approximations; convergence of discretized controls
UR - http://eudml.org/doc/272858
ER -

References

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