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    Asymptotic expansions for high-contrast elliptic equations

    Access Status
    Fulltext not available
    Authors
    Calo, Victor
    Efendiev, Y.
    Galvis, J.
    Date
    2014
    Type
    Journal Article
    
    Metadata
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    Citation
    Calo, V. and Efendiev, Y. and Galvis, J. 2014. Asymptotic expansions for high-contrast elliptic equations. Mathematical Models and Methods in Applied Sciences. 24 (3): pp. 465-494.
    Source Title
    Mathematical Models and Methods in Applied Sciences
    DOI
    10.1142/S0218202513500565
    ISSN
    0218-2025
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51549
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.

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