×

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


MSC:

76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[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
[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
[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
[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
[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
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.