A weak Galerkin generalized multiscale finite element method

Mu, Lin; Wang, Junping; Ye, Xiu

doi:10.1016/j.cam.2016.03.017

Title: A weak Galerkin generalized multiscale finite element method

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Abstract

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.

Authors:: Mu, Lin; Wang, Junping; Ye, Xiu

Publication Date:: Sat Oct 01 00:00:00 EDT 2016

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1675001

Alternate Identifier(s):: OSTI ID: 1311297; OSTI ID: 1358864

Grant/Contract Number:: ERKJE45; AC05-00OR22725

Resource Type:: Published Article

Journal Name:: Journal of Computational and Applied Mathematics

Additional Journal Information:: Journal Name: Journal of Computational and Applied Mathematics Journal Volume: 305 Journal Issue: C; Journal ID: ISSN 0377-0427

Publisher:: Elsevier

Country of Publication:: Belgium

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; weak Galerkin; multiscale; finite element methods; elliptic problems with rapidly oscillating or high contrast coefficients; polyhedral meshes

Citation Formats


                    Mu, Lin, Wang, Junping, and Ye, Xiu. A weak Galerkin generalized multiscale finite element method.  Belgium: N. p., 2016. 
Web.  doi:10.1016/j.cam.2016.03.017.

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                    Mu, Lin, Wang, Junping, & Ye, Xiu. A weak Galerkin generalized multiscale finite element method.  Belgium.  https://doi.org/10.1016/j.cam.2016.03.017

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                    Mu, Lin, Wang, Junping, and Ye, Xiu. Sat .  
"A weak Galerkin generalized multiscale finite element method".  Belgium.  https://doi.org/10.1016/j.cam.2016.03.017.

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@article{osti_1675001,

  title        = {A weak Galerkin generalized multiscale finite element method},

  author       = {Mu, Lin and Wang, Junping and Ye, Xiu},

  abstractNote = {In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.},

  doi          = {10.1016/j.cam.2016.03.017},

  journal      = {Journal of Computational and Applied Mathematics},

  number       = C,

  volume       = 305,

  place        = {Belgium},

  year         = {Sat Oct 01 00:00:00 EDT 2016},

  month        = {Sat Oct 01 00:00:00 EDT 2016}

}

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