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Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities∗

Published online by Cambridge University Press:  27 March 2014

M. Hintermüller ,
R.H.W. Hoppe  and
C. Löbhard
M. Hintermüller
Affiliation:
Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany. [email protected]; [email protected]
R.H.W. Hoppe
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA; [email protected] Institute of Mathematics, University of Augsburg, Universitätsstraße 14, 86152 Augsburg, Germany; [email protected]
C. Löbhard
Affiliation:
Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany. [email protected]; [email protected]
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Abstract

A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical realization of the adaptive concept are provided and a report on numerical tests including the critical cases of biactivity are presented.

Keywords

Adaptive finite element methodC-stationaritygoal-oriented error estimationmathematical programming with equilibrium constraintsoptimal control of variational inequalities
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014 , pp. 524 - 546
Copyright
© EDP Sciences, SMAI, 2014

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