Mixed finite element methods for generalized forchheimer flow in porous media

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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 LJ; L(Ω)) for the pressure.

Original languageEnglish
Pages (from-to)213-228
Number of pages16
JournalNumerical Methods for Partial Differential Equations
Volume21
Issue number2
DOIs
Publication statusPublished - 2005 Mar 1

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

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