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Numerical Methods for a Model for Compressible Miscible Displacement in Porous Media

Jim Douglas, Jr. and Jean E. Roberts
Mathematics of Computation
Vol. 41, No. 164 (Oct., 1983), pp. 441-459
DOI: 10.2307/2007685
Stable URL: http://www.jstor.org/stable/2007685
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Numerical Methods for a Model for Compressible Miscible Displacement in Porous Media
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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 $L^\propto$ are derived for the errors in the approximate solutions for both methods.

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