Internal and subspace correction approximations of implicit variational inequalities

Lori Badea (1) , Marius Cocou (2)

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

The aim of this paper is to study the existence of solutions and some approximations for a class of implicit evolution variational inequalities that represents a generalization of several quasistatic contact problems in elasticity. Using appropriate estimates for the incremental solutions, the existence of a continuous solution and convergence results are proved for some corresponding internal approximation and backward difference scheme. To solve the fully discrete problems, general additive subspace correction algorithms are considered, for which global convergence is proved and some error estimates are established.

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

Lori Badea, Marius Cocou. Internal and subspace correction approximations of implicit variational inequalities. Mathematics and Mechanics of Solids, 2015, 20 (9), pp. 1026-1048/DOI: 10.1177/1081286513514075. ⟨10.1177/1081286513514075⟩. ⟨hal-00949613⟩