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Obstacle problems with cohesion: a hemivariational inequality approach and its efficient numerical solution

Please always quote using this URN:urn:nbn:de:0296-matheon-6814
  • Motivated by an obstacle problem for a membrane subject to cohesion forces, constrained minimization problems involving a non-convex and non-differentiable objective functional representing the total potential energy are considered. The associated first order optimality system leads to a hemi-variational inequality, which can also be interpreted as a special complementarity problem in function space. Besides an analytical investigation of first-order optimality, a primal-dual active set solver is introduced. It is associated to a limit case of a semi-smooth Newton method for a regularized version of the underlying problem class. For the numerical algorithms studied in this paper, global as well as local convergence properties are derived and verified numerically.

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Metadaten
Author:Michael Hintermüller, Victor Kovtunenko, Karl Kunisch
URN:urn:nbn:de:0296-matheon-6814
Referee:Ralf Kornhuber
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/01/28
Release Date:2010/01/27
Tag:
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J40 Variational methods including variational inequalities [See also 47J20]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M29 Methods involving duality
Preprint Number:687
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