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    A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

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    Type
    Article
    Authors
    Efendiev, Yalchin R. cc
    Lazarov, Raytcho D.
    Moon, Minam
    Shi, Ke
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Porous Media SRI Center (NumPor)
    Date
    2014-10-22
    Embargo End Date
    2016-02-02
    Permanent link to this record
    http://hdl.handle.net/10754/566068
    
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    Abstract
    We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.
    Citation
    Efendiev, Y., Lazarov, R., Moon, M., & Shi, K. (2015). A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems. Computer Methods in Applied Mechanics and Engineering, 292, 243–256. doi:10.1016/j.cma.2014.09.036
    Sponsors
    YE's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project. R. Lazarov's research was supported in part by the National Science Foundation (DMS-1016525).
    Publisher
    Elsevier BV
    Journal
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2014.09.036
    Additional Links
    https://manuscript.elsevier.com/S0045782514003594/pdf/S0045782514003594.pdf
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cma.2014.09.036
    Scopus Count
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    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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