APPROXIMATION RESULTS AND SUBSPACE CORRECTION ALGORITHMS FOR IMPLICIT VARIATIONAL INEQUALITIES

作者：Badea Lori^*; Cocou Marius

来源：Discrete and Continuous Dynamical Systems - Series S, 2013, 6(6): 1507-1524.

DOI：10.3934/dcdss.2013.6.1507

• Evolution problems
• implicit variational inequalities
• approximation and existence results
• subspace correction
• domain decomposition
• Schwarz method
• multilevel methods

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.

• 出版日期2013-12