An immersed hybrid difference method for the elliptic interface equation - Jeon, Youngmok (Japan Journal of Industrial and Applied Mathematics, 2022)
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.
Keywords: Difference method; Elliptic interface; Elliptic interface problems; High-order methods; Higher-order methods; Hybrid difference method; Immersed interface; Interface equations; Real transformation; Virtual to real transformation; Elliptic interface problem; Hybrid difference method; Immersed interface; VR transformation