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    A multiscale mortar multipoint flux mixed finite element method

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    Type
    Article
    Authors
    Wheeler, Mary Fanett
    Xue, Guangri
    Yotov, Ivan
    KAUST Grant Number
    KUS-F1-032-04
    Date
    2012-02-03
    Online Publication Date
    2012-02-03
    Print Publication Date
    2012-07
    Permanent link to this record
    http://hdl.handle.net/10754/597327
    
    Metadata
    Show full item record
    Abstract
    In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
    Citation
    Wheeler MF, Xue G, Yotov I (2012) A multiscale mortar multipoint flux mixed finite element method. ESAIM: Mathematical Modelling and Numerical Analysis 46: 759–796. Available: http://dx.doi.org/10.1051/m2an/2011064.
    Sponsors
    partially supported by the NSF-CDI under contract number DMS 0835745, the DOE grant DE-FGO2-04ER25617, and the Center for Frontiers of Subsurface Energy Security under Contract No. DE-SC0001114.supported by Award No. KUS-F1-032-04, made by King Abdullah University of Science and Technology (KAUST).partially supported by the DOE grant DE-FG02-04ER25618, the NSF grant DMS 0813901, and the J. Tinsley Oden Faculty Fellowship, ICES, The University of Texas at Austin.
    Publisher
    EDP Sciences
    Journal
    ESAIM: Mathematical Modelling and Numerical Analysis
    DOI
    10.1051/m2an/2011064
    ae974a485f413a2113503eed53cd6c53
    10.1051/m2an/2011064
    Scopus Count
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    Publications Acknowledging KAUST Support

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