A Finite Difference Method for Elliptic Problems with Implicit Jump Condition

Abstract

In this paper linear elliptic problems with imperfect contact interface are considered, and a second order finite difference method is presented for linear problems, in which implicit jump condition are imposed on the interface. Then, the stability and convergence analysis of the FD scheme are given for the one-dimensional elliptic interface problem. Numerical examples are carried out for the elliptic problems with imperfect contact interfaces, and the results demonstrate that the scheme has second order accuracy for elliptic interface problems of implicit jump conditions with single and multiple imperfect interfaces.