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13-11-2015

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

Authors: Pengtao Sun, Yuzhou Sun

Published in: Journal of Scientific Computing | Issue 1/2016

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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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Title: Asymptotic Analysis and Error Estimates of Mixed Finite Element Method for Brinkman Model
Authors: Pengtao Sun
Yuzhou Sun
Publication date: 13-11-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0131-3

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