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A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media. (English) Zbl 0526.76094

76S05Flows in porous media; filtration; seepage
76M99Basic methods in fluid mechanics
Full Text: EuDML
[1] 1. J. DOUGLAS, Jr., Effective time-stepping methods for the numerical solution of nonlinear parabolic problems, The Mathematics of Finite Eléments and Applications III, MAFELAP 1978, J. R. Whiteman (éd.), Academic Press, 1979. Zbl0435.65095 MR559305 · Zbl 0435.65095
[2] 2. J. DOUGLAS, T. DUPONT and P. PERCELL, A time-stepping method for Galerkin approximations for nonlinear parabolic équations, Numerical Analysis, Dundee 1977, Lecture Notes in Mathematics 630, Springer, 1978. Zbl0381.65058 MR483542 · Zbl 0381.65058
[3] 3. J. DOUGLAS, T. DUPONT and R. E. EWING, Incomplete itération for time-stepping a nonlinear parabolic Galerkin method, SIAM J. Numer. Anal., 16, 1979, pp. 503-522. Zbl0411.65064 MR530483 · Zbl 0411.65064 · doi:10.1137/0716039
[4] 4. J. DOUGLAS, R. E. EWING and M. F. WHEELER, The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Analyse numérique, 17, 1983, pp. 17-33. Zbl0516.76094 MR695450 · Zbl 0516.76094 · eudml:193407
[5] 5. J. DOUGLAS, M. F. WHEELER, B. L. DARLOW and R. P. KENDALL, Self-adaptive finite element simulation of miscible displacement, to appear in SIAM J. Scientific and Statistical Computing. · Zbl 0535.76115
[6] 6. R. E. EWING and T. F. RUSSELL, Efficient time-stepping methods for miscible displacement problems in porous media, SIAM J. Numer. Anal., 19, 1982, pp. 1-67. Zbl0498.76084 MR646594 · Zbl 0498.76084 · doi:10.1137/0719001
[7] 7. R. E. EWING and M. F. WHEELER, Galerkin methods for miscible displacement problems in porous media, SIAM J. Numer. Anal., 17, 1980, pp. 351-365. Zbl0458.76092 MR581482 · Zbl 0458.76092 · doi:10.1137/0717029
[8] 8. C. JOHNSON and V. THOMÉE, Error estimates for some mixed finite element methods for parabolic problems, RAIRO Analyse numérique, 15, 1981, pp.41-78. Zbl0476.65074 MR610597 · Zbl 0476.65074 · eudml:193370
[9] 9. D. W. PEACEMAN, Improved treatment of dispersion in numerical calculation of multidimensional miscible displacement, oc. Pet. Eng. J. (1966), pp. 213-216.
[10] 10. D. W. PEACEMAN, Fundamentals of Numerical Reservoir Simulation, Elsevier, 1977
[11] 11. 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, 1977. Zbl0362.65089 MR483555 · Zbl 0362.65089
[12] 12. T. F. RUSSELL, An incompletely iterated characteristic finite element method for a miscible displacement problem, Thesis, University of Chicago, June 1980.
[13] 13. A. H. SCHATZ, V. THOMÉE and L. WAHLBIN, Maximum norm stability and error estimates in parabolic finite element équations, Comm. Pure Appl. Math., 33, 1980, pp. 265-304. Zbl0414.65066 MR562737 · Zbl 0414.65066 · doi:10.1002/cpa.3160330305
[14] 14. R. SCHOLZ, L \infty -convergence of saddle-point approximations for second order problems, RAIRO Analyse numérique, 11, 1977, pp. 209-216. Zbl0356.35026 MR448942 · Zbl 0356.35026 · eudml:193297