Geodesic
Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state
Charles Brett1 ; Charles M. Elliott1 orcid ; Michael Hintermüller2 ; Caroline Löbhard3
1University of Warwick, Coventry, UK
2Weierstrass-Institut, Berlin, Germany
3Humboldt-Universität zu Berlin, Germany
Interfaces and free boundaries, Tome 17 (2015) no. 1, pp. 21-53

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DOI

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 approximate 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.
DOI : 10.4171/ifb/332
Classification : 49-XX, 65-XX, 90-XX
Mots-clés : Adaptive finite element methods, optimal control of variational inequalities in function space, point-tracking, C-stationarity, goal-oriented error estimation

Charles Brett  1   ; Charles M. Elliott  1   ; Michael Hintermüller  2   ; Caroline Löbhard  3

1 University of Warwick, Coventry, UK
2 Weierstrass-Institut, Berlin, Germany
3 Humboldt-Universität zu Berlin, Germany 
Charles Brett; Charles M. Elliott; Michael Hintermüller; Caroline Löbhard. Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state. Interfaces and free boundaries, Tome 17 (2015) no. 1, pp. 21-53. doi: 10.4171/ifb/332
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     title = {Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state},
     journal = {Interfaces and free boundaries},
     pages = {21--53},
     year = {2015},
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     number = {1},
     doi = {10.4171/ifb/332},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/332/}
}
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