Approximation results and subspace correction algorithms for implicit variational inequalities

Lori Badea; Marius Cocou

doi:10.3934/dcdss.2013.6.1507

Article Contents

2013, Volume 6, Issue 6: 1507-1524. Doi: 10.3934/dcdss.2013.6.1507

This issue Previous Article On damping rates of dissipative KdV equations Next Article Structure of the space of 2D elasticity tensors

Approximation results and subspace correction algorithms for implicit variational inequalities

Lori Badea^1, and
Marius Cocou^2,

1.
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest
2.
LMA, Aix-Marseille University, CNRS, UPR 7051, Centrale Marseille, F-13402 Marseille Cedex 20

Received: May 31, 2012

Revised: August 31, 2012

Published: November 2013

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Abstract

This paper deals with the mathematical analysis and the subspace approximation of a system of variational inequalities representing a unified approach to several quasistatic contact problems in elasticity. Using an implicit time discretization scheme and some estimates, convergence properties of the incremental solutions and existence results are presented for a class of abstract implicit evolution variational inequalities involving a nonlinear operator. To solve the corresponding semi-discrete and the fully discrete problems, some general subspace correction algorithms are proposed, for which global convergence is analyzed and error estimates are established.

Keywords:

Mathematics Subject Classification: Primary: 35K86, 65K15, 65N55; Secondary: 65N12, 65N30.

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