A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
Jim Jr. Douglas; Richard E. Ewing; Mary Fanett Wheeler
- Volume: 17, Issue: 3, page 249-265
- ISSN: 0764-583X
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topDouglas, Jim Jr., Ewing, Richard E., and Wheeler, Mary Fanett. "A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 17.3 (1983): 249-265. <http://eudml.org/doc/193417>.
@article{Douglas1983,
author = {Douglas, Jim Jr., Ewing, Richard E., Wheeler, Mary Fanett},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {time-discretization; elliptic mixed finite element method to pressure and velocity; parabolic Galerkin method to concentration; miscible displacement; time-stepping nonlinear parabolic equations by incomplete iteration; convergence; optimal order error},
language = {eng},
number = {3},
pages = {249-265},
publisher = {Dunod},
title = {A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media},
url = {http://eudml.org/doc/193417},
volume = {17},
year = {1983},
}
TY - JOUR
AU - Douglas, Jim Jr.
AU - Ewing, Richard E.
AU - Wheeler, Mary Fanett
TI - A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1983
PB - Dunod
VL - 17
IS - 3
SP - 249
EP - 265
LA - eng
KW - time-discretization; elliptic mixed finite element method to pressure and velocity; parabolic Galerkin method to concentration; miscible displacement; time-stepping nonlinear parabolic equations by incomplete iteration; convergence; optimal order error
UR - http://eudml.org/doc/193417
ER -
References
top- 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. 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. 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. 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. 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. 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. 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. 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. D. W. PEACEMAN, Improved treatment of dispersion in numerical calculation of multidimensional miscible displacement, oc. Pet. Eng. J. (1966), pp. 213-216.
- 10. D. W. PEACEMAN, Fundamentals of Numerical Reservoir Simulation, Elsevier, 1977
- 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. T. F. RUSSELL, An incompletely iterated characteristic finite element method for a miscible displacement problem, Thesis, University of Chicago, June 1980.
- 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. R. SCHOLZ, -convergence of saddle-point approximations for second order problems, RAIRO Analyse numérique, 11, 1977, pp. 209-216. Zbl0356.35026MR448942
Citations in EuDML Documents
top- Todd Arbogast, On the simulation of incompressible, miscible displacement in a naturally fractured petroleum reservoir
- Yuting Wei, Stabilized finite element methods for miscible displacement in porous media
- Mohamed Mandari, Mohamed Rhoudaf, Ouafa Soualhi, The generalized finite volume SUSHI scheme for the discretization of the peaceman model
- Zhangxin Chen, Expanded mixed finite element methods for linear second-order elliptic problems, I
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