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

Document Type

Article

Publication Date

11-13-2015

Publication Title

Journal of Scientific Computing

Volume

68

Issue

1

First page number:

116

Last page number:

142

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.

Keywords

Brinkman model; Forcheimer model; Navier-Stokes-Darcy coupling; Mixed finite element method; Asymptotic analysis; Optimal convergence

Disciplines

Mathematics

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