A mathematical model and numerical solution of interface problems for steady state heat conduction
Year: 2006
Type: article
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), x ∈ Ω ⊂ ℝ2, with discontinuous coefficient k = k(x). We analyse two types of jump (or contact) conditions across the interfaces and of the layered medium Ω : = Ω1 ∪ Ωδ ∪ Ω2. 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.
Authors: Z. Muradoglu Seyidmamedov, Ebru Ozbilge
Institutions: Kocaeli Üniversitesi, İzmir University of Economics
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,550
OpenAlex ID: W2078490990