Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities∗. (7th April 2014)

• Record Type: Journal Article
• Authors: Hintermüller, M.; Hoppe, R.H.W.; Löbhard, C.
• Is Part Of: ESAIM. Volume 20:Number 2(2014:Apr.)
• Page Start: 524
• Page End: 546
• Publication Date: 2014-04-07
• Subjects: Adaptive finite element method, -- C-stationarity, -- goal-oriented error estimation, -- mathematical programming with equilibrium constraints, -- optimal control of variational inequalities; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013074
• Languages: English
• ISSNs: 1292-8119

Abstract

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.