Generalized multiscale finite element method. Symmetric interior penalty coupling

JOURNAL OF COMPUTATIONAL PHYSICS

卷:255

Article

Efendiev, Y.^1,2  Galvis, J.³  Lazarov, R.¹  Moon, M.¹  Sarkis, M.^4,5 

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] King Abdullah Univ Sci & Technol, SRI Ctr Numer Porous Media, Thuwal 239556900, Saudi Arabia

[3] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia

[4] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA

[5] Inst Nacl Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

关键词: Multiscale finite element method;    Discontinuous Galerkin;    Snapshot spaces;    Upscaling;   

DOI  :  10.1016/j.jcp.2013.07.028

来源: Elsevier

【 摘 要 】

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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