椭圆界面问题的高阶差分格式

High-Order Finite Difference Scheme for Elliptic Interface Problem

构造混合边界条件下椭圆界面问题的一个高阶数值格式.在求解区域内部及界面处采用四阶逼近,边界处采用三阶数值格式,得到一个整体四阶精度的求解格式.数值实验证明了格式的高精度及有效性.

In this paper,we propose a high-order finite difference scheme for elliptic interface problems with mixed boundary conditions.The fourth-order approximation is adopted in the solution area and the interface,while a third-order numerical scheme is adopted on the boundary,we obtain a solution scheme with global fourth order accuracy.Numerical experiments are given to illustrate the high accuracy and effectiveness of our scheme.