A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media

 Access to full text

 Full (PDF)

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. Zbl0435.65095MR559305
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. Zbl0381.65058MR483542
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. Zbl0411.65064MR530483
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. Zbl0516.76094MR695450
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. Zbl0535.76115
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. Zbl0498.76084MR646594
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. Zbl0458.76092MR581482
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. Zbl0476.65074MR610597
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. Zbl0362.65089MR483555
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. Zbl0414.65066MR562737
14. 14. R. SCHOLZ, $L_{\infty }$-convergence of saddle-point approximations for second order problems, RAIRO Analyse numérique, 11, 1977, pp. 209-216. Zbl0356.35026MR448942

1. Todd Arbogast, On the simulation of incompressible, miscible displacement in a naturally fractured petroleum reservoir
2. Yuting Wei, Stabilized finite element methods for miscible displacement in porous media
3. Mohamed Mandari, Mohamed Rhoudaf, Ouafa Soualhi, The generalized finite volume SUSHI scheme for the discretization of the peaceman model
4. Zhangxin Chen, Expanded mixed finite element methods for linear second-order elliptic problems, I