An expanded mixed finite element method for generalized Forchheimer flows in porous media

Akif Ibragimov, Thinh T. Kieu

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We study the expanded mixed finite element method applied to degenerate parabolic equations with the Dirichlet boundary condition. The equation is considered a prototype of the nonlinear Forchheimer equation for slightly compressible fluid flow in porous media. The bounds for the solutions are established. In both continuous and discrete time procedures, utilizing the monotonicity properties of Forchheimer equation and the boundedness of solutions, we establish the error estimates in L2-norm for solutions, divergence of the vector variable in several Lebesgue norms. A numerical example using the lowest order Raviart–Thomas (RT0) mixed element confirms our theoretical results regarding convergence rates.

Original languageEnglish
Pages (from-to)1467-1483
Number of pages17
JournalComputers and Mathematics with Applications
Volume72
Issue number6
DOIs
StatePublished - Sep 1 2016

Keywords

  • Error estimates
  • Expanded mixed finite element
  • Generalized Forchheimer equations
  • Nonlinear degenerate parabolic equations

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