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

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• 作者：Akif Ibragimov^a ; ^{akif.ibraguimov@ttu.edu" class="auth_mail" title="E-mail the corresponding author} ; Thinh T. Kieu^b ; ^{thinh.kieu@ung.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Expanded mixed finite element ; Nonlinear degenerate parabolic equations ; Generalized Forchheimer equations ; Error estimates
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：72
• 期：6
• 页码：1467-1483
• 全文大小：506 K

文摘

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$L^2$-norm for solutions, divergence of the vector variable in several Lebesgue norms. A numerical example using the lowest order Raviart–Thomas (RT₀$R{T}_0$) mixed element confirms our theoretical results regarding convergence rates.