We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded and measurable, which may admit rough microstructures. As a by-product of the energy estimate, we derive the rate of convergence in L$^{d/(d-1)}-$norm.

翻译：我们得出多尺度有限元素法的最佳能源误差估计值,该方法采用过量抽样技术,适用于具有快速波动周期系数的椭圆形系统,前提是这些系数是受约束和可测量的,可能接受粗微结构。 作为能源估计的副产品,我们得出了L$d/(d-1)-norm的趋同率。