This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for the proposed method. The theoretical results are conformed by various numerical experiments.

翻译：本文采用一种结合$H^1$插值的局部正交分解（LOD）方法来求解多尺度椭圆问题。该方法无需任何尺度分离假设。我们给出了所提方法的先验误差估计，并通过多种数值实验验证了理论结果。