论文标题
约束能量最小化通用多尺度有限元法，以使其不均匀边界价值问题具有高对比度系数
Constraint energy minimizing generalized multiscale finite element method for inhomogeneous boundary value problems with high contrast coefficients
论文作者
论文摘要
在本文中，我们开发了最小化通用多尺度有限元法（CEM-GMSFEM）的约束能量，以使用不均匀的Dirichlet，Neumann和Robin边界条件，将椭圆形的部分微分方程和较高的对比度属性来自椭圆机操作员和Robin边界条件的系数出现。通过仔细构建CEM-GMSFEM的多尺寸基础，我们介绍了两个操作员$ \ Mathcal {d}^m $和$ \ Mathcal {n}^m $，这些{n}^m $用于处理不均匀的Dirichlet和Neumann边界价值，并且也被证明并被证明是与造成比较的比例相比，并且与过度的较高较大的比例相比。我们提供了先验错误估计，并表明过采样层是控制数值错误的关键因素。进行了一系列实验，这些结果也反映了我们方法的可靠性，即使对比度高。
In this article we develop the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, and the high contrast property emerges from the coefficients of elliptic operators and Robin boundary conditions. By careful construction of multiscale bases of the CEM-GMsFEM, we introduce two operators $\mathcal{D}^m$ and $\mathcal{N}^m$ which are used to handle inhomogeneous Dirichlet and Neumann boundary values and are also proved to converge independently of contrast ratios as enlarging oversampling regions. We provide a priori error estimate and show that oversampling layers are the key factor in controlling numerical errors. A series of experiments are conducted, and those results reflect the reliability of our methods even with high contrast ratios.
