中文摘要：

利用修正的有限体积方法求解带有间断系数的泊松方程，改进是对基于笛卡尔坐标系下的调和平均系数进行的。数值实验表明新格式二阶逐点收敛并且在界面处具有二阶精度，新方法较已有的求解不连续扩散系数的算术平均法和调和平均法，特别是在系数跳跃较大的情况下更具优势。

英文摘要：

In this paper, a new modified finite volume method is presented to solve the elliptic equations with discontinuous coefficients. This method allows discontinuities of the solution and normal derivatives on the interface inside the domain on a Cartesian grid, From experiment results, this scheme is second-order point-wise convergence and approximates the fluxes to second-order accuracy. At the same time, the numerical results show that the new scheme is much more accurate than the known schemes which use arithmetic and harmonic averaging in solving interface problems, especially in the cases of large jumps of coefficient.