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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 $ {L^2}$ and almost optimal-order estimates in $ {L^\infty }$ are obtained for the errors in the approximate solutions under the condition that $ h_p^{2k + 2}{(\log h_c^{ - 1})^{1/2}} \to 0$. This condition is much weaker than one given earlier by Douglas and Roberts for the same model. Furthermore, we obtain the $ {L^\infty }({L^2}(\Omega ))$-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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Article copyright: © Copyright 1991 American Mathematical Society

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