A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such process numerically. In this paper we introduce a FEHMM scheme for multiscale elliptic problems based on nonconforming spaces. In particular we use the noconforming element with the periodic boundary condition introduced in the companion paper. Theoretical analysis derives a priori error estimates in the standard Sobolev norms. Several numerical results which confirm our analysis are provided.

翻译：以有限要素为基础的有限元素杂变多尺度法(FEHMM)使得能够用数字模拟这一过程。在本文件中,我们引入了一个基于不兼容空间的多尺度椭圆问题的FEHMM计划。特别是我们使用与配套文件中引入的定期边界条件不相符的元素。理论分析在标准Sobolev规范中得出了先验错误估计。提供了数项结果证实我们的分析。