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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 39.4 (2010): 827-854. <http://eudml.org/doc/194288>.

@article{Kunisch2010,

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},

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

language = {eng},

month = {3},

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/194288},

volume = {39},

year = {2010},

}

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

DA - 2010/3//

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.; active sets

UR - http://eudml.org/doc/194288

ER -

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