A high order generalized finite difference method for solving the anisotropic elliptic interface problem in static and moving systems

Abstract

In this paper, a high order meshless numerical scheme based on the Generalized Finite Difference Method (GFDM) is proposed to analyze the anisotropic elliptic interface problem. The GFDM has an advantage in dealing with some anisotropic elliptic problems with complex interfaces, interface conditions with the jump of derivatives. Four problems with eight examples are provided to verify the existence of the good performance of the GFDM for anisotropic elliptic interface problems, including that the simplicity, accuracy, and stability in static and moving systems. Especially, GFDM has the tolerance of the complexity of interface shape, the interface movement and the large jump.