Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints

Eduardo Casas

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

Abstract

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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∞ 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.

How to cite

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Casas, 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 (2010): 345-374. <http://eudml.org/doc/90652>.

@article{Casas2010,
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∞ 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.; distributed control; numerical approximation; error estimates},
language = {eng},
month = {3},
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/90652},
volume = {8},
year = {2010},
}

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
DA - 2010/3//
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∞ 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.; distributed control; numerical approximation; error estimates
UR - http://eudml.org/doc/90652
ER -

References

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