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.
Author: | Michael Hintermüller, Victor Kovtunenko, Karl Kunisch |
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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 |