We propose an immersed hybrid difference (IHD) method for elliptic interface problems. An essential feature of the IHD method lies in the VR(virtual to real) transformation, which makes it possible to derive accurate finite difference approximations with functions of low regularity on interface cells. The VR transformation is consisting of the interface conditions in addition to the consistency equations, which are derived from the governing equation. The method is easy to be implemented and high order methods are conveniently derived. Numerical tests on several types of interfaces with low and high order methods are presented, which demonstrates efficiency of the IHD method. Numerical analysis for the one dimensional case is provided.
This author was supported by NRF 2018R1D1A1A09082082.The author would like express sincere thanks to Prof. Son-Young Yi at department of mathematics, UTEP for careful reading the manuscript and suggesting invaluable comments, which improved the early version of the manuscript a lot.
