Mixed finite element methods for generalized Forchheimer flow in porous media

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 approxi...

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Bibliographic Details
Published inNumerical methods for partial differential equations Vol. 21; no. 2; pp. 213 - 228
Main Author Park, Eun-Jae
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2005
Subjects
error estimates
Forchheimer's law
mixed methods
non-Darcy flow
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Summary: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 L∞(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. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005
Bibliography:istex:E3443E616C5DF070802B5E5E00D1CDBFF32CAFEC
KOSEF - No. 1999-2-103-001-5
Com2Mac-KOSEF
ark:/67375/WNG-W0GDCZXP-2
ArticleID:NUM20035
AMS subject classifications: 65M15, 65M60, 76A05, 76M10, 76S05
ISSN:0749-159X
1098-2426
DOI:10.1002/num.20035