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Lions’s work on the Schwarz alternating method for convex minimization problems is generalized to a certain non-smooth situation where the non-differentiable 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 L2(). 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. © 1997 by John Wiley & Sons, Ltd.

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