论文标题
有效的数值方法，用于可靠的上限和下限均质参数
Efficient numerical method for reliable upper and lower bounds on homogenized parameters
论文作者
论文摘要
介绍了椭圆形偏差操作员有效系数的保证两侧边界的数值程序。上限是通过问题的变分制和应用有限元方法以标准方式获得的。为了获得下限，我们制定了双重变异问题，并还采用有限元方法引入适当的近似空间。我们处理3D设置，到目前为止，文献中很少考虑。该程序的理论依据得到了说明性示例和支持。
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the problem and by applying the finite element method. To obtain the lower bounds we formulate the dual variational problem and introduce appropriate approximation spaces employing the finite element method as well. We deal with the 3D setting, which has been rarely considered in the literature so far. The theoretical justification of the procedure is presented and supported with illustrative examples.
