Article ID Journal Published Year Pages File Type
500312 Computer Methods in Applied Mechanics and Engineering 2007 12 Pages PDF
Abstract

We develop a new 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.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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