# Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

- Volume: 39, Issue: 4, page 827-854
- ISSN: 0764-583X

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topKunisch, Karl, and Stadler, Georg. "Generalized Newton methods for the 2D-Signorini contact problem with friction in function space." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.4 (2005): 827-854. <http://eudml.org/doc/245546>.

@article{Kunisch2005,

abstract = {The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional semi-smooth Newton method for the solution of the problem with given friction. The resulting algorithm is locally superlinearly convergent and can be interpreted as active set strategy. Combining the method with an augmented lagrangian method leads to convergence of the iterates to the solution of the original problem. Comprehensive numerical tests discuss, among others, the dependence of the algorithm’s performance on material and regularization parameters and on the mesh. The remarkable efficiency of the method carries over to the Signorini problem with Coulomb friction by means of fixed point ideas.},

author = {Kunisch, Karl, Stadler, Georg},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Signorini contact problems; Coulomb and Tresca friction; linear elasticity; semi-smooth Newton method; Fenchel dual; augmented lagrangians; complementarity system; active sets; augmented Lagrangians},

language = {eng},

number = {4},

pages = {827-854},

publisher = {EDP-Sciences},

title = {Generalized Newton methods for the 2D-Signorini contact problem with friction in function space},

url = {http://eudml.org/doc/245546},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Kunisch, Karl

AU - Stadler, Georg

TI - Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 4

SP - 827

EP - 854

AB - The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional semi-smooth Newton method for the solution of the problem with given friction. The resulting algorithm is locally superlinearly convergent and can be interpreted as active set strategy. Combining the method with an augmented lagrangian method leads to convergence of the iterates to the solution of the original problem. Comprehensive numerical tests discuss, among others, the dependence of the algorithm’s performance on material and regularization parameters and on the mesh. The remarkable efficiency of the method carries over to the Signorini problem with Coulomb friction by means of fixed point ideas.

LA - eng

KW - Signorini contact problems; Coulomb and Tresca friction; linear elasticity; semi-smooth Newton method; Fenchel dual; augmented lagrangians; complementarity system; active sets; augmented Lagrangians

UR - http://eudml.org/doc/245546

ER -

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