DOMAIN DECOMPOSITION METHOD WITH NONOVERLAPPING SUBDOMAINS FOR ELLIPTIC VARIATIONAL-INEQUALITIES USING LAGRANGE MULTIPLIERS

DDM are thoroughly studied in the case of the linear boundary-value pr oblems for partial differential equations (PDE's). On the other hand t here are feu results concerning these methods for free boundary proble ms (FBP's). We, mention the articles [1-5] dealing with the overlappin g and non-overlapping DDM's for the elliptic variational inequalities (VI's) and some evolutionary FBP's. One of the motivation to use the D DM especially for FBP's is as follows. Usually we can localize the fre e boundaries on the basis of a priori and/or a posteriori information and divide the initial domain into two groups of subdomains in such a way that a solution for the problem under consideration satisfies a PD E in the first group of the subdomains while a FBP in. the second one. Thus we can use the different approaches to solve the problems in the subdomains (using grid refinement, multigrids, efficient linear algor ithms etc.) The aim of the report is to develop the non-overlapping DD M for the stationary VI's using a general framework.