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：我们重新推导了应用超采样技术的多尺度有限元法对于具有快速振荡周期系数的椭圆系统的最优能量误差估计,其前提是系数有界且可测,允许存在粗糙的微观结构。作为能量估计的副产品,我们推导了L$^{d/(d-1)}$范数下的收敛速度。