Mixed finite element methods for compressible miscible displacement in porous media

Authors:
So-Hsiang Chou and Qian Li

Journal:
Math. Comp. **57** (1991), 507-527

MSC:
Primary 76M10; Secondary 65N30, 76N10, 76S05

MathSciNet review:
1094942

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Abstract: A differential system describing compressible miscible displacement in a porous medium is given. The concentration equation is treated by a Galerkin method and the pressure equation is treated by a parabolic mixed finite element method. Optimal-order estimates in and almost optimal-order estimates in are obtained for the errors in the approximate solutions under the condition that . This condition is much weaker than one given earlier by Douglas and Roberts for the same model. Furthermore, we obtain the -estimates for the time-derivatives of the concentration and the pressure, which were not given by the above authors. In addition, we also consider newer mixed spaces in two or three dimensions.

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1094942-7

Article copyright:
© Copyright 1991
American Mathematical Society