Mixed finite element methods for generalized forchheimer flow in porous media

Eun Jae Park

doi:10.1002/num.20035

Mixed finite element methods for generalized forchheimer flow in porous media

Eun Jae Park

School of Mathematics and Computing

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

78 Citations (Scopus)

Abstract

Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single-phase fluid in a porous medium in ℝ^d, d ≤3, subject to Forchhheimer's law - a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L ^∞(J; L²(Ω)) and in V(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L^∞J; L^∞(Ω)) for the pressure.

Original language	English
Pages (from-to)	213-228
Number of pages	16
Journal	Numerical Methods for Partial Differential Equations
Volume	21
Issue number	2
DOIs	https://doi.org/10.1002/num.20035
Publication status	Published - 2005 Mar

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1002/num.20035

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abstract = "Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single-phase fluid in a porous medium in ℝd, d ≤3, subject to Forchhheimer's law - a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L ∞(J; L2(Ω)) and in V(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L∞J; L∞(Ω)) for the pressure.",

keywords = "Error estimates, Forchheimer's law, Mixed methods, Non-Darcy flow",

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AU - Park, Eun Jae

PY - 2005/3

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N2 - Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single-phase fluid in a porous medium in ℝd, d ≤3, subject to Forchhheimer's law - a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L ∞(J; L2(Ω)) and in V(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L∞J; L∞(Ω)) for the pressure.

AB - Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single-phase fluid in a porous medium in ℝd, d ≤3, subject to Forchhheimer's law - a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L ∞(J; L2(Ω)) and in V(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L∞J; L∞(Ω)) for the pressure.

KW - Error estimates

KW - Forchheimer's law

KW - Mixed methods

KW - Non-Darcy flow

UR - https://www.scopus.com/pages/publications/14744293611

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

Mixed finite element methods for generalized forchheimer flow in porous media

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