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

J. D. Audu; F. Fairag; K. Mustapha

doi:10.1016/j.cam.2018.12.009

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

J. D. Audu^*
, F. Fairag
, K. Mustapha

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 L ^m and L ^{[Formula presented]} respectively are obtained for any m∈(1,2]. Numerical examples are also presented to confirm the rate of convergence.

Original language	English
Pages (from-to)	191-203
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	353
DOIs	https://doi.org/10.1016/j.cam.2018.12.009
State	Published - Jun 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

Convergence
Error bound
Generalized Darcy–Forchheimer
Mixed finite element
Porous media

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2018.12.009

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title = "Mixed finite element analysis for generalized Darcy–Forchheimer model in porous media",

abstract = " 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 L m and L [Formula presented] respectively are obtained for any m∈(1,2]. Numerical examples are also presented to confirm the rate of convergence.",

keywords = "Convergence, Error bound, Generalized Darcy–Forchheimer, Mixed finite element, Porous media",

author = "Audu, \{J. D.\} and F. Fairag and K. Mustapha",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2019",

month = jun,

doi = "10.1016/j.cam.2018.12.009",

language = "English",

volume = "353",

pages = "191--203",

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T1 - Mixed finite element analysis for generalized Darcy–Forchheimer model in porous media

AU - Audu, J. D.

AU - Fairag, F.

AU - Mustapha, K.

PY - 2019/6

Y1 - 2019/6

N2 - 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 L m and L [Formula presented] respectively are obtained for any m∈(1,2]. Numerical examples are also presented to confirm the rate of convergence.

AB - 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 L m and L [Formula presented] respectively are obtained for any m∈(1,2]. Numerical examples are also presented to confirm the rate of convergence.

KW - Convergence

KW - Error bound

KW - Generalized Darcy–Forchheimer

KW - Mixed finite element

KW - Porous media

UR - https://www.scopus.com/pages/publications/85059872398

U2 - 10.1016/j.cam.2018.12.009

DO - 10.1016/j.cam.2018.12.009

M3 - Article

AN - SCOPUS:85059872398

SN - 0377-0427

VL - 353

SP - 191

EP - 203

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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