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Upscaled HDG Methods for Brinkman Equations with High-Contrast Heterogeneous Coefficient

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Abstract

In this paper, we present new upscaled HDG methods for Brinkman equations in the context of high-contrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that depend on the high-contrast coefficient weakly. Due to the heterogeneity of the problem, a huge global system will be produced after the numerical discretization of HDG method. Thanks to the upscaled structure of the proposed methods, we are able to reduce the huge global system onto the skeleton of the coarse mesh only while still capturing important fine scale features of this problem. The finite element space over the coarse mesh is irrelevant to the fine scale computation. This feature makes our proposed method very attractive. Several numerical examples are presented to support our theoretical findings.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, London, SW7 2AZ, UK

    Guanglian Li

  2. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA

    Ke Shi

Authors
  1. Guanglian Li
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  2. Ke Shi
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Correspondence to Ke Shi.

Additional information

Dedicated to Bernardo Cockburn on the occasion of his 60-th anniversary.

G. Li acknowledges the support from the Hausdorff Center for Mathematics, Bonn and the Royal Society via the Newton International Fellowship. Part of this work was done during G. Li’s research visit at IPAM for the long program: Computational Issues in Oil Field Applications. Ke Shi is partially supported by SRFP grant from the Research Foundation, Old Dominion University. As a convention the names of the authors are alphabetically ordered. Both authors contributed equally in this article. The authors thank Yalchin Efendiev and Raytcho Lazarov (Texas A&M University, College Station) for fruitful discussions.

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Li, G., Shi, K. Upscaled HDG Methods for Brinkman Equations with High-Contrast Heterogeneous Coefficient. J Sci Comput 77, 1780–1800 (2018). https://doi.org/10.1007/s10915-018-0725-7

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  • DOI: https://doi.org/10.1007/s10915-018-0725-7

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