An adaptive GMsFEM for high-contrast flow problems

Tsz Shun Eric CHUNG Yalchin Efendiev Guanglian Li

TBD mathscidoc:1910.43462

Journal of Computational Physics, 273, 54-76, 2014.9
In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. This error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic equation with multiscale high-contrast coefficients. The GMsFEM, which has recently been introduced in [13], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space,(2) the construction of the offline space, and (3) the construction of the online space (the latter for parameter-dependent problems). In [13], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we
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  title={An adaptive GMsFEM for high-contrast flow problems},
  author={Tsz Shun Eric CHUNG, Yalchin Efendiev, and Guanglian Li},
  booktitle={Journal of Computational Physics},
Tsz Shun Eric CHUNG, Yalchin Efendiev, and Guanglian Li. An adaptive GMsFEM for high-contrast flow problems. 2014. Vol. 273. In Journal of Computational Physics. pp.54-76.
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