Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints
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@example.com.
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.
Mathematics Subject Classification: 49J20 / 49K20 / 49M05 / 65K10
Key words: Distributed control / state constraints / semilinear elliptic equation / numerical approximation / finite element method / error estimates.
© EDP Sciences, SMAI, 2002