Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Approximation results and subspace correction algorithms for implicit variational inequalities

Pages: 1507 - 1524, Volume 6, Issue 6, December 2013      doi:10.3934/dcdss.2013.6.1507

       Abstract        References        Full Text (401.1K)       Related Articles       

Lori Badea - Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania (email)
Marius Cocou - LMA, Aix-Marseille University, CNRS, UPR 7051, Centrale Marseille, F-13402 Marseille Cedex 20, France (email)

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:  Evolution problems, implicit variational inequalities, approximation and existence results, subspace correction, domain decomposition, Schwarz method, multilevel methods.
Mathematics Subject Classification:  Primary: 35K86, 65K15, 65N55; Secondary: 65N12, 65N30.

Received: June 2012;      Revised: September 2012;      Available Online: April 2013.