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Asymptotic Analysis and Error Estimates of Mixed Finite Element Method for Brinkman Model

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Abstract

In this paper, we study a one-continuum model approach, so-called Brinkman model, to deal with Navier–Stokes–Darcy coupling problem in which the fluid flow exist in both the open channels and porous media. A parameter re-scaling technique is used to reformulate the traditional Brinkman model to a new one in order to investigate its asymptotic accuracy to Stokes and Darcy’s equations, respectively. We attain the convergence theorem in quantitative measure with respect to the dimensionless permeability parameter. We also analyze the error estimates of mixed finite element method for Brinkman model and Forchheimer model, and obtain the optimal convergence rates for both velocity and pressure. Numerical experiments validate the convergence results with respect to the permeability parameter and mesh size for both Brinkman model and Forchheimer model.

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Acknowledgments

P. Sun is supported by NSF Grant DMS-1418806.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV, 89154, USA

    Pengtao Sun & Yuzhou Sun

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  1. Pengtao Sun
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  2. Yuzhou Sun
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Correspondence to Pengtao Sun.

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Sun, P., Sun, Y. Asymptotic Analysis and Error Estimates of Mixed Finite Element Method for Brinkman Model. J Sci Comput 68, 116–142 (2016). https://doi.org/10.1007/s10915-015-0131-3

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