# 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

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topCasas, 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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- [10] I. Hlaváček, M. Křížek and J. Malý, On Galerkin approximations of quasilinear nonpotential elliptic problem of a nonmonotone type. J. Math. Anal. Appl.184 (1994) 168–189. Zbl0802.65113
- [11] L. Liu, M. Křížek and P. Neittaanmäki, Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type. Appl. Math.41 (1996) 467–478. Zbl0870.65096
- [12] R. Rannacher and R. Scott, Some optimal error estimates for piecewise finite element approximations. Math. Comp.38 (1982) 437–445. Zbl0483.65007MR645661
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