Upstream weighting and mixed finite elements in the simulation of miscible displacements

Jérôme Jaffre; Jean E. Roberts

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1985)

  • Volume: 19, Issue: 3, page 443-460
  • ISSN: 0764-583X

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Jaffre, Jérôme, and Roberts, Jean E.. "Upstream weighting and mixed finite elements in the simulation of miscible displacements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 19.3 (1985): 443-460. <http://eudml.org/doc/193455>.

@article{Jaffre1985,
author = {Jaffre, Jérôme, Roberts, Jean E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite element method; incompressible miscible displacements; pressure equation; discontinuous upstream weighting scheme; concentration equation; Error estimates},
language = {eng},
number = {3},
pages = {443-460},
publisher = {Dunod},
title = {Upstream weighting and mixed finite elements in the simulation of miscible displacements},
url = {http://eudml.org/doc/193455},
volume = {19},
year = {1985},
}

TY - JOUR
AU - Jaffre, Jérôme
AU - Roberts, Jean E.
TI - Upstream weighting and mixed finite elements in the simulation of miscible displacements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1985
PB - Dunod
VL - 19
IS - 3
SP - 443
EP - 460
LA - eng
KW - finite element method; incompressible miscible displacements; pressure equation; discontinuous upstream weighting scheme; concentration equation; Error estimates
UR - http://eudml.org/doc/193455
ER -

References

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  1. 1. F. BREZZI, On the existence, uniqueness and approximation of saddle-point problem arising from Lagrangien multipliers. R.A.I.R.O., Anal. Numér. 2 (1974), pp. 129-151 Zbl0338.90047MR365287
  2. 2. G. CHAVENT, G. COHEN, M. DUPUY, J JAFFRE, I. RIBERA, Simulation of two dimensional water flooding using mixed finite elements, SPEJ. 24 (1984), pp. 382-390. 
  3. 3. J. DOUGLAS Jr., R. E. EWING, M. F. WHEELER, The approximation of the pressure by a mixed method in the simulation of miscible displacement, R.A.I.R.O., Anal. Numér. 17 (1983), pp. 17-33. Zbl0516.76094MR695450
  4. 4. J. DOUGLAS Jr., J. E. ROBERTS, Numerical methods for a model for compressible miscible displacement in porous media, Math. Comp. 41 (1983), pp. 441-459. Zbl0537.76062MR717695
  5. 5. R. E. EWING, M. F. WHEELER, Galerkin methods for miscible displacement problem in porous media, SIAM J. Numér. Anal. 17 (1980), pp. 351-365. Zbl0458.76092MR581482
  6. 6. M. FORTIN, Résolution numérique des équations de Navier Stokes par des éléments finis du type mixte, Rapport INRIA n° 184, INRIA Le Chesnay (1976). 
  7. 7. J JAFFRE, Éléments finis mixtes et décentrage pour les équations de diffusion-convection, Calcolo 23 (1984), pp. 171-197. Zbl0562.65077MR799619
  8. 8. P. JOLY, La méthode des éléments finis mixtes appliquée au problème de diffusion-convection, Thèse de 3e cycle, Université Pierre-et-Marie Curie, Paris (1982). 
  9. 9. C. JOHNSON, V. THOMÉE, Error estimates for some mixed finite element methods for parabolic type problems, R.A.I.R.O., Anal. Numér., 15 (1981), pp. 41-78. Zbl0476.65074MR610597
  10. 10. P LESAINT, P. A. RAVIART, On a finite element method for solving the neutron transport equation. Mathematical Aspect of Finite Elements in Partial Differential Equations, Ed. Carl de Boor, Academic Press (1974), pp. 89-123. Zbl0341.65076MR658142
  11. 11. P. A. RAVIART, J. M. THOMAS, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of the Finite Element Method, Eds. I. Galligani and E. Magenes, Lecture Notes in Mathematics 606, Springer Verlag (1977), pp. 292-315. Zbl0362.65089MR483555
  12. 12. T. F. RUSSELL, Finite elements with characteristics for two-component incompressible miscible displacement, 6th SPE Symposium on Reservoir Simulation, New Orléans, SPE 10500 (1982). 
  13. 13. M. F. WHEELER, B. L. DARLOW, Interior penalty Galerkin methods for miscible displacement problems in porous media, Computational Methods in Nonlinear Mechanics, Ed. J. T. Oden, North Holland (1980). Zbl0444.76081MR576923

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