# The approximation of the pressure by a mixed method in the simulation of miscible displacement

Jim Jr. Douglas; Richard E. Ewing; Mary Fanett Wheeler

- Volume: 17, Issue: 1, page 17-33
- ISSN: 0764-583X

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topDouglas, Jim Jr., Ewing, Richard E., and Wheeler, Mary Fanett. "The approximation of the pressure by a mixed method in the simulation of miscible displacement." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 17.1 (1983): 17-33. <http://eudml.org/doc/193407>.

@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 = {miscible displacement; concentration; pressure; mixed finite element method; standard Galerkin method; optimal order estimates; sources and sinks},

language = {eng},

number = {1},

pages = {17-33},

publisher = {Dunod},

title = {The approximation of the pressure by a mixed method in the simulation of miscible displacement},

url = {http://eudml.org/doc/193407},

volume = {17},

year = {1983},

}

TY - JOUR

AU - Douglas, Jim Jr.

AU - Ewing, Richard E.

AU - Wheeler, Mary Fanett

TI - The approximation of the pressure by a mixed method in the simulation of miscible displacement

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 1983

PB - Dunod

VL - 17

IS - 1

SP - 17

EP - 33

LA - eng

KW - miscible displacement; concentration; pressure; mixed finite element method; standard Galerkin method; optimal order estimates; sources and sinks

UR - http://eudml.org/doc/193407

ER -

## References

top- 1. D.N. ARNOLD, An interior penalty finite element method with discontinuous éléments, Thesis, University of Chicago, June 1979.
- 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. Zbl0338.90047MR365287
- 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. 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. 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
- 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. Zbl0458.76092MR581482
- 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. Zbl0551.76079MR790511
- 8. D. W. PEACEMAN, Improved treatment of dispersion in numerical calculation of multidimensional miscible displacement, Soc. Pet. Eng. J. (1966), pp. 213-216.
- 9. D. W. PEACEMAN, Fundamentals of Numerical Reservoir Simulation, Elsevier Publishing Co., 1977.
- 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. Zbl0362.65089MR483555
- 11. T. F. RUSSELL, An incompletely iterated characteristic finite element method fora miscible displacement problem, Thesis, University of Chicago, June 1980.
- 12. P. H. SAMMON, Numerical approximations for a miscible displacement process inporous media, to appear. Zbl0608.76084
- 13. J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrideset mixtes, Thèse, Université Pierre et Marie Curie, 1977.
- 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. Zbl0444.76081MR576923

## Citations in EuDML Documents

top- Jérôme Jaffre, Jean E. Roberts, Upstream weighting and mixed finite elements in the simulation of miscible displacements
- Jim Jr. Douglas, Richard E. Ewing, Mary Fanett Wheeler, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
- 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
- Ricardo G. Durán, Error analysis in ${L}^{p}\u2a7dp\u2a7d\infty $, for mixed finite element methods for linear and quasi-linear elliptic problems
- Zhangxin Chen, Expanded mixed finite element methods for linear second-order elliptic problems, I

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