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On averaging of the non‐periodic conductivity coefficient using two‐scale extensions
Author(s) -
Laptev Vsevolod,
Belouettar Salim
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510316
Subject(s) - homogeneous , scale (ratio) , extension (predicate logic) , mathematics , flow (mathematics) , mathematical analysis , porous medium , materials science , thermodynamics , physics , porosity , computer science , geometry , quantum mechanics , programming language , composite material
We consider a second order elliptic equation with known rapidly oscillated coefficient. The equation appears to describe such problems as heat transfer in composite materials, flow in non‐homogeneous porous media as well as in many others. For the periodic coefficient the averaging procedure is well known. The non‐periodic case is still a challenging problem. We present a two‐scale extension approach and apply it on one numerical example in 2D. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)