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Domain decomposition for model heterogeneous anisotropic problem
Author(s) -
Kwak D. Y.,
Nepomnyaschikh S. V.,
Pyo H. C.
Publication year - 2002
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/nla.315
Subject(s) - domain decomposition methods , mathematics , sobolev space , domain (mathematical analysis) , partial differential equation , finite element method , anisotropy , boundary value problem , decomposition , trace (psycholinguistics) , boundary (topology) , a priori and a posteriori , focus (optics) , fictitious domain method , decomposition method (queueing theory) , mathematical analysis , discrete mathematics , ecology , linguistics , philosophy , physics , epistemology , quantum mechanics , biology , optics , thermodynamics
Abstract The main focus of this paper is to suggest a domain decomposition method for finite element approximations of elliptic problems with anisotropic coefficients in domains consisting of anisotropic shape rectangles. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used for a priori estimates of the stability with respect to boundary conditions, and also play very important role in constructing and investigating effective domain decomposition methods. The trace theorem for anisotropic rectangles with anisotropic grids is the main tool in this paper to construct domain decomposition preconditioners. Copyright © 2002 John Wiley & Sons, Ltd.