期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 255, 期 -, 页码 1-15出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.07.028
关键词
Multiscale finite element method; Discontinuous Galerkin; Snapshot spaces; Upscaling
资金
- US DoD
- DOE
- NSF [DMS 0934837, DMS 0724704, DMS 0811180, DMS 1016525]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1016525] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0934837] Funding Source: National Science Foundation
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 L-2-norm and a boundary weighted L-2-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. (c) 2013 Elsevier Inc. All rights reserved.
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