High-order meshless method based on the generalized finite difference method for 2D and 3D elliptic interface problems

In this article, a high-order meshless method based on the generalized finite difference method (GFDM) is proposed to deal with the elliptic interface problem. The present method is capable of treating complex interfaces with non-homogeneous jump conditions to obtain high-order accuracy. The operation to improve the convergence order is only increasing the order of Taylor series expansion in the GFDM. Numerical examples show the L∞, L2 and H1 errors of this method can obtain 2nth order convergence by using 2nth order Taylor series expansion.