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Mathematical Problems in Engineering
Volume 2006, Article ID 20898, 18 pages
http://dx.doi.org/10.1155/MPE/2006/20898

A mathematical model and numerical solution of interface problems for steady state heat conduction

1Applied Mathematical Sciences Research Center and Department of Mathematics, Kocaeli University, Umuttepe Campus, Izmit - Kocaeli 43800, Turkey
2Department of Mathematics, Faculty of Science and Literature, Izmir University of Economics, 156 Sakarya Avenue, Balcova - Izmir 35330, Turkey

Received 28 March 2006; Revised 1 July 2006; Accepted 16 July 2006

Copyright © 2006 Z. Muradoglu Seyidmamedov and Ebru Ozbilge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study interface (or transmission) problems arising in the steady state heat conduction for layered medium. These problems are related to the elliptic equation of the form Au:=(k(x)u(x))=F(x), xΩ2, with discontinuous coefficient k=k(x). We analyse two types of jump (or contact) conditions across the interfaces Γδ=Ω1Ωδ and Γδ+=ΩδΩ2 of the layered medium Ω:=Ω1ΩδΩ2. An asymptotic analysis of the interface problem is derived for the case when the thickness (2δ>0) of the layer (isolation) Ωδ tends to zero. For each case, the local truncation errors of the used conservative finite difference scheme are estimated on the nonuniform grid. A fast direct solver has been applied for the interface problems with piecewise constant but discontinuous coefficient k=k(x). The presented numerical results illustrate high accuracy and show applicability of the given approach.