Numerical methods for a model for compressible miscible displacement in porous media
Authors:
Jim Douglas and Jean E. Roberts
Journal:
Math. Comp. 41 (1983), 441459
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 and essentially optimal order estimates in are derived for the errors in the approximate solutions for both methods.
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 R. E. Ewing & M. F. Wheeler, "Galerkin methods for miscible displacement problems in porous media," SIAM J. Numer. Anal., v. 17, 1980, pp. 351365. MR 581482 (83d:76035)
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 R. E. Ewing & M. F. Wheeler, "Galerkin methods for miscible displacement problems with point sources and sinksunit mobility ratio case. (To appear.)
 [9]
 C. I. Goldstein & R. Scott, "Optimal estimates for some Galerkin methods for the Dirichlet problem," SIAM J. Numer. Anal. (To appear.)
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 C. Johnson & V. Thomée, "Error estimates for some mixed finite element methods for parabolic type problems," RAIRO Anal. Numér., v. 15, 1981, pp. 4178. MR 610597 (83c:65239)
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 J. A. Nitsche, Convergence of Finite Element Approximation, Proc. Second Conference on Finite Elements, Rennes, France, 1975. MR 568857 (81e:65058)
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 D. W. Peaceman, Fundamentals of Numerical Reservoir Simulation, Elsevier, New York, 1977.
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 D. W. Peaceman, "Improved treatment of dispersion in numerical calculation of multidimensional miscible displacement," Soc. Pet. Eng. J., 1966, pp. 213216.
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 P. A. Raviart & J. M. Thomas, "A mixed finite element method for 2nd order elliptic problems," Mathematical Aspects of the Finite Element Method, Lecture Notes in Math., Vol. 606, SpringerVerlag, Berlin and New York, 1977. MR 0483555 (58:3547)
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 J. M. Thomas, Sur l'Analyse Numérique des Méthodes d'Éléments Finis Hybrides et Mixtes, Thèse, Université Pierre et Marie Curie, Paris, 1977.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307176953
PII:
S 00255718(1983)07176953
Article copyright:
© Copyright 1983
American Mathematical Society
