Generalized Multiscale Finite Element Methods with energy minimizing oversampling

Chung, Eric; Efendiev, Yalchin; Leung, Wing Tat

doi:10.1002/nme.5958

Title: Generalized Multiscale Finite Element Methods with energy minimizing oversampling

Journal Article · Wed Sep 19 00:00:00 EDT 2018 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5958· OSTI ID:1611502

^[1]; Efendiev, Yalchin ^[2]; Leung, Wing Tat ^[2]

Chinese Univ. of Hong Kong (Hong Kong)
Texas A & M Univ., College Station, TX (United States)

Summary In this paper, we propose a general concept for constructing multiscale basis functions within Generalized Multiscale Finite Element Method, which uses oversampling and stable decomposition. The oversampling refers to using larger regions in constructing multiscale basis functions and stable decomposition allows estimating the local errors. The analysis of multiscale methods involves decomposing the error by coarse regions, where each error contribution is estimated. In this estimate, we often use oversampling techniques to achieve a fast convergence. We demonstrate our concepts in the mixed, the Interior Penalty Discontinuous Galerkin, and Hybridized Discontinuous Galerkin discretizations. One of the important features of the proposed basis functions is that they can be used in online Generalized Multiscale Finite Element Method, where one constructs multiscale basis functions using residuals. In these problems, it is important to achieve a fast convergence, which can be guaranteed if we have a stable decomposition. In our numerical results, we present examples for both offline and online multiscale basis functions. Our numerical results show that one can achieve a fast convergence when using online basis functions. Moreover, we observe that coupling using Hybridized Discontinuous Galerkin provides a better accuracy compared with Interior Penalty Discontinuous Galerkin, which is due to using multiscale glueing functions.

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Research Organization:: Texas A & M Univ., College Station, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); Qatar National Research Fund; Russian Federation Government; Chinese University of Hong Kong

Grant/Contract Number:: SC0010713; FG02-13ER26165; 1620318; 7-1482-1278; N 14.Y26.31.0013; 2017-18

OSTI ID:: 1611502

Alternate ID(s):: OSTI ID: 1476939

Journal Information:: International Journal for Numerical Methods in Engineering, Vol. 117, Issue 3; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 6 works

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