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An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Kieweg;  Yuri Iliash;  Ronald H. W. Hoppe;  Michael Hintermüller — 2008

ESAIM: Control, Optimisation and Calculus of Variations

We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...

An error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Hintermüller;  Ronald H.W. Hoppe;  Yuri Iliash;  Michael Kieweg — 2007

ESAIM: Control, Optimisation and Calculus of Variations

We present an error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide a bulk...

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