论文标题
交错的DG方法，带有小边缘，用于骨折的多孔介质中的达西流动
Staggered DG method with small edges for Darcy flows in fractured porous media
论文作者
论文摘要
在本文中，我们介绍并分析了一种在相当通用的网格上断裂的多孔介质中的darcy流交错的盖尔金方法。分别为散装区域和断裂分别利用了交错的不连续的Galerkin方法和具有适当包含界面条件的标准符合有限元法。我们当前的分析削弱了对多边形网格的通常假设，该假设可以将更通用的网格（例如任意边缘边缘的元素）整合到我们的理论框架中。我们通过利用RITZ投影来证明所有变量的最佳收敛估计值$ l^2 $错误。重要的是，我们的误差估计显示在渗透率系数的异质性和各向异性方面完全稳健。进行了几个数值实验，包括具有小边缘和各向异性网格的网格，以确认理论发现。最后，我们的方法应用于未固定网格的框架中。
In this paper, we present and analyze a staggered discontinuous Galerkin method for Darcy flows in fractured porous media on fairly general meshes. A staggered discontinuous Galerkin method and a standard conforming finite element method with appropriate inclusion of interface conditions are exploited for the bulk region and the fracture, respectively. Our current analysis weakens the usual assumption on the polygonal mesh, which can integrate more general meshes such as elements with arbitrarily small edges into our theoretical framework. We prove the optimal convergence estimates in $L^2$ error for all the variables by exploiting the Ritz projection. Importantly, our error estimates are shown to be fully robust with respect to the heterogeneity and anisotropy of the permeability coefficients. Several numerical experiments including meshes with small edges and anisotropic meshes are carried out to confirm the theoretical findings. Finally, our method is applied in the framework of unfitted mesh.
