Domain decomposition for a non-smooth convex minimization problem and its application to plasticity

P.L. Lions's work on the Schwarz alternating method for convex minimization problems is generalized to a certain non-smooth situation where the non-diierentiable part of the functionals is additive and independent with respect to the decomposition. Such functionals arise naturally in plasticity where the material law is a variational inequality formulated in L 2 ((). The application to plasticity with hardening is sketched and gives contraction numbers which are independent of the discretization parameter h and of a possible regularization of the non-smooth material law. 1. Introduction Domain decomposition is proved to be an important tool for parallel computations in the numerical analysis of partial diierential equations. The Schwarz method does converge for many diierent types of problems because of two reasons: the rst is that it has a variational interpretation and the second one is its interpretation in terms of the maximum principle L, p.2]. Motivated by the study of elastoplasticity (see