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

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

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1983)

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

How to cite

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Douglas, 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

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  1. 1. D.N. ARNOLD, An interior penalty finite element method with discontinuous éléments, Thesis, University of Chicago, June 1979. 
  2. 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. 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. 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. 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. 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. 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. 8. D. W. PEACEMAN, Improved treatment of dispersion in numerical calculation of multidimensional miscible displacement, Soc. Pet. Eng. J. (1966), pp. 213-216. 
  9. 9. D. W. PEACEMAN, Fundamentals of Numerical Reservoir Simulation, Elsevier Publishing Co., 1977. 
  10. 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. 11. T. F. RUSSELL, An incompletely iterated characteristic finite element method fora miscible displacement problem, Thesis, University of Chicago, June 1980. 
  12. 12. P. H. SAMMON, Numerical approximations for a miscible displacement process inporous media, to appear. Zbl0608.76084
  13. 13. J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrideset mixtes, Thèse, Université Pierre et Marie Curie, 1977. 
  14. 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

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  1. Jérôme Jaffre, Jean E. Roberts, Upstream weighting and mixed finite elements in the simulation of miscible displacements
  2. 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
  3. Todd Arbogast, On the simulation of incompressible, miscible displacement in a naturally fractured petroleum reservoir
  4. Yuting Wei, Stabilized finite element methods for miscible displacement in porous media
  5. Ricardo G. Durán, Error analysis in L p p , for mixed finite element methods for linear and quasi-linear elliptic problems
  6. Zhangxin Chen, Expanded mixed finite element methods for linear second-order elliptic problems, I

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