Approximation results and subspace correction algorithms for implicit variational inequalities

Lori Badea (1) , Marius Cocou (2)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 M&S - Matériaux et Structures

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.

Mots clés: multilevel methods; Evolution problems; implicit variational inequalities; approximation and existence results; subspace correction; domain decomposition; Schwarz method; multilevel methods.

Domaines: Mécanique des solides [physics.class-ph]; Analyse numérique [math.NA]

Lori Badea, Marius Cocou. Approximation results and subspace correction algorithms for implicit variational inequalities. Discrete and Continuous Dynamical Systems - Series S, 2013, 6 (6), pp.1507-1524. ⟨10.3934/dcdss.2013.6.1507⟩. ⟨hal-00949611⟩