论文标题
$ p_1 $ - 具有周期性边界条件的不合格四边形有限元元素空间：第二部分。应用于不合格的异质多尺度方法
$P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method
论文作者
论文摘要
均质化方法是大约解决多尺度椭圆问题的有效策略之一。基于有限元元素的有限元元素异质多尺度方法（FEHMM）可以通过数值模拟此类过程。在本文中，我们介绍了基于不合格空间的多尺度椭圆问题的FEHMM方案。特别是，我们将Noconormenting元素与伴侣纸中引入的周期性边界条件一起使用。理论分析得出了标准Sobolev规范中的先验误差估计。提供了一些确认我们分析的数值结果。
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.
