Adaptive variational multiscale methods based on a posteriori error estimation:: Energy norm estimates for elliptic problems
Adaptive variational multiscale methods based on a posteriori error estimation:: Energy norm estimates for elliptic problems
复制标题
DOI：
10.1016/j.cma.2006.08.019
复制
发表时间：
2007-01-01
影响因子：
7.2
通讯作者：
Malqvist, Axel
中科院分区：
文献类型：
--
作者：
Larson, Mats G.;Malqvist, Axel
我们发展了一种新的自适应多尺度有限元方法，它使用变分多尺度框架和系统的技术来逼近解的细尺度部分。细尺度近似为解耦局部问题的解的和，这些解在粗网格单元的精细网格划分上进行数值求解。可以增加元素块的大小以控制由局部化引起的误差。我们推导了能量范数下的后验误差估计，它反映了关键的离散化参数：粗网格大小、细网格大小和面片大小的依赖关系。基于后验误差估计，我们提出了一种自动调整这些参数的自适应算法。最后，通过不同的数值算例说明了该方法在实际中的应用。(C)2007 Elsevier B.V.保留所有权利。
We develop anew adaptive multiscale finite element method using the variational multiscale framework together with a systematic technique for approximation of the fine scale part of the solution. The fine scale is approximated by a sum of solutions to decoupled localized problems, which are solved numerically on a fine grid partition of a patch of coarse grid elements. The sizes of the patches of elements may be increased to control the error caused by localization. We derive an a posteriori error estimate in the energy norm which captures the dependency of the crucial discretization parameters: the coarse grid mesh size, the fine grid mesh size, and the sizes of the patches. Based on the a posteriori error estimate we present an adaptive algorithm that automatically tunes these parameters. Finally, we show how the method works in practice by presenting various numerical examples. (c) 2007 Elsevier B.V. All rights reserved.