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Domain decomposition for a non‐smooth convex minimization problem and its application to plasticity
Author(s) -
Carstensen Carsten
Publication year - 1997
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199705/06)4:3<177::aid-nla106>3.0.co;2-b
Subject(s) - mathematics , differentiable function , discretization , minification , regularization (linguistics) , plasticity , variational inequality , regular polygon , domain decomposition methods , effective domain , contraction (grammar) , mathematical analysis , calculus (dental) , mathematical optimization , convex analysis , convex optimization , finite element method , geometry , computer science , physics , dentistry , artificial intelligence , medicine , thermodynamics
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 L 2 (Ω). 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 John Wiley & Sons, Ltd.