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A Dual-Weighted Residual Approach to Goal-Oriented Adaptivity for Optimal Control of Elliptic Variational Inequalities

By Michael (Prof.) Hintermüller, Ronald H. W. (Prof. Dr.) Hoppe and Caroline Löbhard


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

Topics: Optimale Kontrolle, Elliptische Variationsungleichung, Fehlerabschätzung, Finite-Elemente-Methode, ddc:510
Year: 2012
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