Publications

Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling

Bibliography:

Y. Efendiev, J. Galvis, M. Moon, R. Lazarov and M. Sarkis, Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling, Journal of Computational Physics. Volume 255, 15 December 2013, Pages 1–15.

Authors:

Y. Efendiev, J. Galvis, M. Moon, R. Lazarov and M. Sarkis

Keywords:

discontinuous Galerkin, multiscale, finite element

Year:

2013

Abstract:

Motivated by applications to numerical simulation 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 three different finite element spaces on the coarse mesh. 
The first space is based on a local eigenvalue problem that uses a weighted L2norm for computing the "mass" matrix. The second space is generated by amending the eigenvalue problem of the first case with a term related to the penalty. The third choice is based on generation of a large space of snapshots and subsequent selection of a subspace of a reduced dimension. 
The approximation with these 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.

ISSN:

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