Approximation results and subspace correction algorithms for implicit variational inequalities

Lori Badea 1 Marius Cocou 2, *
* Corresponding author
2 M&S - Matériaux et Structures
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
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.
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Lori Badea, Marius Cocou. Approximation results and subspace correction algorithms for implicit variational inequalities. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2013, 6 (6), pp.1507-1524. 〈10.3934/dcdss.2013.6.1507〉. 〈hal-00949611〉

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