# Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 345-374
- ISSN: 1292-8119

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topCasas, Eduardo. "Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 345-374. <http://eudml.org/doc/244707>.

@article{Casas2002,

abstract = {The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the $L^\infty $ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states.},

author = {Casas, Eduardo},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {distributed control; state constraints; semilinear elliptic equation; numerical approximation; finite element method; error estimates},

language = {eng},

pages = {345-374},

publisher = {EDP-Sciences},

title = {Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints},

url = {http://eudml.org/doc/244707},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Casas, Eduardo

TI - Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 345

EP - 374

AB - The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the $L^\infty $ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states.

LA - eng

KW - distributed control; state constraints; semilinear elliptic equation; numerical approximation; finite element method; error estimates

UR - http://eudml.org/doc/244707

ER -

## References

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## Citations in EuDML Documents

top- Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
- Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
- Pedro Merino, Fredi Tröltzsch, Boris Vexler, Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
- Eduardo Casas, Fredi Tröltzsch, Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
- Eduardo Casas, Mariano Mateos, Boris Vexler, New regularity results and improved error estimates for optimal control problems with state constraints

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