Galerkin finite element method for generalized Forchheimer equation of slightly compressible fluids in porous media |
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| Authors: | Thinh Kieu |
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| Affiliation: | Department of Mathematics, University of North Georgia, Gainesville Campus, Oakwood, GA, U.S.A. |
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| Abstract: | We consider the generalized Forchheimer flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear degenerate parabolic equation for the density. We study Galerkin finite elements method for the initial boundary value problem. The existence and uniqueness of the approximation are proved. A prior estimates for the solutions in  , time derivative in  and gradient in  , with a∈(0,1) are established. Error estimates for the density variable are derived in several norms for both continuous and discrete time procedures. Numerical experiments using backward Euler scheme confirm the theoretical analysis regarding convergence rates. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | porous media immersible flow error analysis Galerkin finite element nonlinear degenerate parabolic equations generalized Forchheimer equations numerical analysis |
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, time derivative in 
and gradient in 
, with a∈(0,1) are established. Error estimates for the density variable are derived in several norms for both continuous and discrete time procedures. Numerical experiments using backward Euler scheme confirm the theoretical analysis regarding convergence rates. Copyright © 2017 John Wiley & Sons, Ltd.