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Error Estimates for the Numerical Approximation of SemilinearElliptic Control Problems with 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; [email protected].
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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.

Keywords

Distributed controlstate constraintssemilinear elliptic equationnumerical approximationfinite element methoderror estimates.
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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