Generalized multiscale finite element method. Symmetric interior penalty coupling

Abstract
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

Citation
Efendiev, Y., Galvis, J., Lazarov, R., Moon, M., & Sarkis, M. (2013). Generalized multiscale finite element method. Symmetric interior penalty coupling. Journal of Computational Physics, 255, 1–15. doi:10.1016/j.jcp.2013.07.028

Acknowledgements
Y.E.'s work is partially supported by the US DoD, DOE and NSF (DMS 0934837, DMS 0724704, and DMS 0811180).J. Galvis would like to acknowledge partial support from DOE. R. Lazarov's research was supported in parts by NSF (DMS 1016525).

Publisher
Elsevier BV

Journal
Journal of Computational Physics

DOI
10.1016/j.jcp.2013.07.028

arXiv
1302.7071

Additional Links
http://arxiv.org/abs/arXiv:1302.7071v1

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