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Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics. (English) Zbl 0545.76131

See the preview in Zbl 0535.76116.

MSC:

76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0535.76116
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References:

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[4] Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO Anal. Numér., 2, 129-151 (1974) · Zbl 0338.90047
[5] Douglas, J., Simulation of miscible displacement in porous media by a modified method of characteristic procedure, (Numerical Analysis. Numerical Analysis, Lecture Notes in Mathematics, 912 (1982), Springer: Springer Berlin), Dundee 1981
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[9] Douglas, J.; Ewing, R. E.; Wheeler, M. F., A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, RAIRO Anal. Numér., 17, 249-265 (1983) · Zbl 0526.76094
[10] Douglas, J.; Russell, T. F., Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal., 19, 871-885 (1982) · Zbl 0492.65051
[11] Dupont, T.; Fairweather, G.; Johnson, J. P., Three-level Galerkin methods for parabolic equations, SIAM J. Numer. Anal., 11, 392-410 (1974) · Zbl 0313.65107
[12] Ewing, R. E.; Russell, T. F., Efficient time-stepping methods for miscible displacement problems in porous media, SIAM J. Numer. Anal., 19, 1-67 (1982) · Zbl 0498.76084
[13] Ewing, R. E.; Russell, T. F.; Wheeler, M. F., Simulation of miscible displacement using mixed methods and a modified method of characteristics, (Proceedings, Seventh SPE Symposium on Reservoir Simulation. Proceedings, Seventh SPE Symposium on Reservoir Simulation, Paper SPE 12241 (1983), Society of Petroleum Engineers: Society of Petroleum Engineers Dallas, TX), 71-81
[14] Ewing, R. E.; Wheeler, M. F., Galerkin methods for miscible displacement problems with point sources and Sinks—unit mobility ratio case, (Proceedings of the Special Year in Numerical Analysis. Proceedings of the Special Year in Numerical Analysis, Lecture Notes No. 20 (1981), Univ. of Maryland: Univ. of Maryland College Park), 151-174
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[17] Russell, T. F., An incompletely iterated characteristic finite element method for a miscible displacement problem, (Ph.D. Thesis (1980), University of Chicago)
[18] SIAM J. Numer. Anal., submitted.; SIAM J. Numer. Anal., submitted.
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