Generalized multiscale finite element method. Symmetric interior penalty coupling
Type
ArticleKAUST Department
Numerical Porous Media SRI Center (NumPor)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2013-12Preprint Posting Date
2013-02-28Permanent link to this record
http://hdl.handle.net/10754/563114
Metadata
Show full item recordAbstract
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.2013.07.028Sponsors
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 BVJournal
Journal of Computational PhysicsarXiv
1302.7071Additional Links
http://arxiv.org/abs/arXiv:1302.7071v1ae974a485f413a2113503eed53cd6c53
10.1016/j.jcp.2013.07.028