中文摘要：

通过基于变系数可分离变量情形下限定扰动边界条件求解子问题，使多尺度基函数能很好地捕获模型问题的微观信息；该数值模拟方法仅在粗网格水平即可得到精确、收敛的结果。研究表明，运用多尺度有限元法进行复杂的多尺度数值模拟，既可节约计算资源又能保证计算的精度。

英文摘要：

Based on the separated variables coefficients we refine the oscillatory boundary condition in the sub-problem. The corresponding multi-scale basis functions can capture the microcosmic information of the model problem. The numerical simulation method is able to obtain accurate and convergent results on the coarse grids easily, and can not only reduce the computational costs, but also ensure the computational accuracy.