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

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

  • Volume: 17, Issue: 3, page 249-265
  • ISSN: 0764-583X

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Douglas, 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

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  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 -convergence of saddle-point approximations for second order problems, RAIRO Analyse numérique, 11, 1977, pp. 209-216. Zbl0356.35026MR448942

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