A finite difference method for elliptic problems with implicit jump condition. (English) Zbl 1513.65276
Summary: 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.
MSC:
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 35R35 | Free boundary problems for PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
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