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