论文标题
与速度消除的混合有限元方法的自适应通用多尺度近似
Adaptive generalized multiscale approximation of a mixed finite element method with velocity elimination
论文作者
论文摘要
在本文中，我们提出了离线和在线自适应富集算法，以消除速度消除的混合有限元方法的广义多尺度近似，以解决高对比度和异构多孔培养基中的地下流量问题。我们对这两种自适应方法的收敛性进行了理论分析，这表明足够的初始基础函数（属于离线空间）会导致更快的收敛速率。提供了一系列数值示例，以突出两种自适应方法的性能，并验证理论分析。离线和在线自适应方法都是有效的，可以大大减少相对错误。此外，在线自适应方法的性能通常比离线自适应方法更好，因为在线基础功能包含重要的全局信息，例如远处效应，而远处效果无法通过离线基础功能捕获。数值结果还表明，使用合适的初始多尺度空间，其中包括所有离线基础函数，对应于离线阶段局部光谱分解的相对较小特征值，在线富集的收敛速率与渗透性对比无关。
In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and heterogeneous porous media. We give the theoretical analysis for the convergence of these two adaptive methods, which shows that sufficient initial basis functions (belong to the offline space) leads to a faster convergence rate. A series of numerical examples are provided to highlight the performance of both these two adaptive methods and also validate the theoretical analysis. Both offline and online adaptive methods are effective that can reduce the relative error substantially. In addition, the online adaptive method generally performs better than the offline adaptive method as online basis functions contain important global information such as distant effects that cannot be captured by offline basis functions. The numerical results also show that with a suitable initial multiscale space that includes all offline basis functions corresponding to relative smaller eigenvalues of local spectral decompositions in the offline stage, the convergence rate of the online enrichment is independent of the permeability contrast.
