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Error Estimates for the Numerical Approximationof SemilinearElliptic Control Problemswith Finitely Many State Constraints

Published online by Cambridge University Press:  15 August 2002

Eduardo Casas
Eduardo Casas*
Affiliation:
Dpt. Matemática Aplicada y Ciencias de la Computación, E.T.S.I.I y T., Universidad de Cantabria, Av. Los Castros s/n, 39005 Santander, Spain; eduardo.casas@unican.es.
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Abstract

The goal of this paper is to derive some error estimates for thenumerical discretization of some optimal control problems governedby semilinear elliptic equations with bound constraints on thecontrol and a finitely number of equality and inequality stateconstraints. We prove some error estimates for the optimalcontrols in the L ∞ norm and we also obtain error estimatesfor the Lagrange multipliers associated to the state constraintsas well as for the optimal states and optimal adjoint states.

Keywords

Distributed controlstate constraintssemilinear elliptic equationnumerical approximationfinite element methoderror estimates.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002, pp. 345 - 374
Copyright
© EDP Sciences, SMAI, 2002

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References

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