2015-01-01Zeitschriftenartikel DOI: 10.4171/IFB/332
Mesh Adaptivity in Optimal Controlof Elliptic Variational Inequalities with Point-Tracking of the State
An adaptive finite element method is developed for a class of optimal control problems with elliptic variational inequality constraints and objective functionals defined on the space of continuous functions, necessitated by a point-tracking requirement with respect to the state variable. A suitable first order stationarity concept is derived for the problem class via a penalty technique. The dual-weighted residual approach for goal-oriented adaptive finite elements is applied and relies on the stationarity system. It yields primal residuals weighted by approxi- mate dual quantities and vice versa as well as complementarity mismatch errors. A report on numerical tests, including the critical case of biactivity, completes this work.
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