Mixed finite element analysis for generalized Darcy–Forchheimer model in porous media

We considered mixed finite element discretization of generalized Darcy–Forchheimer model in a two or three dimensional porous domain, using a piecewise constant and continuous piecewise linear finite elements. The existence, uniqueness, stability and convergence of the discrete solution are establis...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-06, Vol.353, p.191-203
Main Authors: Audu, J.D., Fairag, F., Mustapha, K.
Format: Article
Language:English
Subjects:
Convergence
Error bound
Generalized Darcy–Forchheimer
Mixed finite element
Porous media
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Summary:We considered mixed finite element discretization of generalized Darcy–Forchheimer model in a two or three dimensional porous domain, using a piecewise constant and continuous piecewise linear finite elements. The existence, uniqueness, stability and convergence of the discrete solution are established. The error estimates for the velocity and pressure in Lm and Lm+1m respectively are obtained for any m∈(1,2]. Numerical examples are also presented to confirm the rate of convergence.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2018.12.009