1 research outputs found
A mathematical model and numerical solution of interface problems for steady state heat conduction
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 Γδ−=Ω1∩Ωδ and Γδ+=Ωδ∩Ω2 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