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The approximation of the pressure by a mixed method in the simulation of miscible displacement. (English) Zbl 0516.76094

MSC:
76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
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References:
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[2] 2. F. BREZZI, On the existence, uniqueness and approximation of saddle-point problems a rising from Lagrangian multipliers, R.A.I.R.O., Anal Numér. 2(1974), pp. 129-151. Zbl0338.90047 MR365287 · Zbl 0338.90047 · eudml:193255
[3] 3. J. Jr. DOUGLAS and T. DUPONT, Interior penalty procedure for elliptic and parabolic Galerkin methods, Computing Methods in Applied Science, Lecture Notesin Physics 58, Springer-Verlag, 1976. MR440955
[4] 4. J. Jr. DOUGLAS, M. F. WHEELER, B. L. DARLOW and R. P. KENDALL, Self-adaptivefinite element simulation of miscible displacement in porous media, to appear in SIAM J. Sci. Stat. Computing.
[5] 5. J. Jr. DOUGLAS, Simulation of miscible displacement in porous media by a modifiedmethod of characteristics procedure, to appear in the proceedings of the 1981 Dundee Conference on Numerical Analysis. Zbl0476.76100 · Zbl 0476.76100
[6] 6. R. E. EWING and M. F. WHEELER, Galerkin methods for miscible displacementproblems in poróus media, SIAM J. Numer. Anal. 17 (1980), pp. 351-365. Zbl0458.76092 MR581482 · Zbl 0458.76092 · doi:10.1137/0717029
[7] 7. R. E. EWING and M. F. WHEELER, Galerkin methods for miscible displacement problems with point sources and sinks, unit mobility ratio case, to appear. Zbl0551.76079 MR790511 · Zbl 0551.76079
[8] 8. D. W. PEACEMAN, Improved treatment of dispersion in numerical calculation of multidimensional miscible displacement, Soc. Pet. Eng. J. (1966), pp. 213-216.
[9] 9. D. W. PEACEMAN, Fundamentals of Numerical Reservoir Simulation, Elsevier Publishing Co., 1977.
[10] 10. P. A. RAVIART and J. M. THOMAS, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of the Finite Element Method,Lecture Notes in Mathematics 606, Springer-Verlag, 1977. Zbl0362.65089 MR483555 · Zbl 0362.65089
[11] 11. T. F. RUSSELL, An incompletely iterated characteristic finite element method fora miscible displacement problem, Thesis, University of Chicago, June 1980.
[12] 12. P. H. SAMMON, Numerical approximations for a miscible displacement process inporous media, to appear. Zbl0608.76084 · Zbl 0608.76084 · doi:10.1137/0723034
[13] 13. J. M. THOMAS, Sur l’analyse numérique des méthodes d’éléments finis hybrideset mixtes, Thèse, Université Pierre et Marie Curie, 1977.
[14] 14. M.F. WHEELER and B. L. DARLOW, Interior penalty Galerkin methods for miscible displacement problems in porous media, Computational Methods in NonlinearMechanics (J. T. Oden, éd.), North-Holland Publishing Co., 1980. Zbl0444.76081 MR576923 · Zbl 0444.76081
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