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Mesh adaptivity and error estimates applied to a regularized p ‐Laplacian constrainted optimal control problem for multiple quantities of interest
Author(s) -
Endtmayer Bernhard,
Langer Ulrich,
Neitzel Ira,
Wick Thomas,
Wollner Winnifried
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900231
Subject(s) - laplace operator , constraint (computer aided design) , mathematical optimization , mathematics , residual , laplace transform , optimal control , polygon mesh , work (physics) , dual (grammatical number) , computer science , algorithm , mathematical analysis , geometry , physics , art , literature , thermodynamics
Abstract In this work, we derive goal‐oriented error estimates and mesh adaptivity for multiple quantities of interest for optimal control problems with the regularized p ‐Laplace equation as constraint. We apply the dual‐weighted residual method to the reduced formulation, and combine several quantities of interest. Finally, we present a numerical example with p = 10.