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Numerical methods for a model for compressible miscible displacement in porous media

Authors: Jim Douglas and Jean E. Roberts
Journal: Math. Comp. 41 (1983), 441-459
MSC: Primary 65M60; Secondary 76S05
MathSciNet review: 717695
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Abstract: A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The system is consistent with the usual model for incompressible miscible displacement. Two finite element procedures are introduced to approximate the concentration of one of the fluids and the pressure of the mixture. The concentration is treated by a Galerkin method in both procedures, while the pressure is treated by either a Galerkin method or by a parabolic mixed finite element method. Optimal order estimates in $ {L^2}$ and essentially optimal order estimates in $ {L^\infty }$ are derived for the errors in the approximate solutions for both methods.

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