A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact (Journal of Computational Mathematics, 2024)
In this paper two dimensional elliptic interface problem with imperfect contact is considered, which is featured by the implicit jump condition imposed on the imperfect contactinterface, and the jumping quantity of the unknown is related to the flux across the interface. A finite difference method is constructed for the 2D elliptic interface problemswith straight and curve interface shapes. Then, the stability and convergence analysis aregiven for the constructed scheme. Further, in particular case, it is proved to be monotone.Numerical examples for elliptic interface problems with straight and curve interface shapesare tested to verify the performance of the scheme. The numerical results demonstratethat it obtains approximately second-order accuracy for elliptic interface equations withimplicit jump condition.
Keywords: Finite difference method; Elliptic interface problem; Imperfect contact.