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Volumn 27, Issue 2, 1997, Pages 225-242

From Single-Phase to Compositional Flow: Applicability of Mixed Finite Elements

Author keywords

Finite elements; Fractional flow; Mixed methods; Multiphase flow; Porous media

Indexed keywords

DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; MULTIPHASE FLOW; PERFORMANCE; POROUS MATERIALS;

EID: 0031141903     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006507816183     Document Type: Article
Times cited : (37)

References (28)
  • 1
    • 0002600676 scopus 로고
    • On the solvability of boundary value problems for degenerate two-phase porous flow equations in Russian
    • Antoncev, S.: On the solvability of boundary value problems for degenerate two-phase porous flow equations in Russian, Dinamika Splošnoii Sredy Vyp. 10 (1972), 28-53.
    • (1972) Dinamika Splošnoii Sredy Vyp. , vol.10 , pp. 28-53
    • Antoncev, S.1
  • 3
    • 0003720236 scopus 로고    scopus 로고
    • Analysis of the inexact Uzawa algorithm for saddle point problems
    • Texas A& M University
    • Bramble, J., Pasciak, J. and Vassilev, A.: Analysis of the inexact Uzawa algorithm for saddle point problems, ISC-94-09-MATH Technical Report, Texas A& M University.
    • ISC-94-09-MATH Technical Report
    • Bramble, J.1    Pasciak, J.2    Vassilev, A.3
  • 6
    • 0026398228 scopus 로고
    • A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems
    • Chavent, G. and Roberts, J. E.: A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems, Adv. Water Resour. 14 (1991), 329-348.
    • (1991) Adv. Water Resour. , vol.14 , pp. 329-348
    • Chavent, G.1    Roberts, J.E.2
  • 7
    • 0039486183 scopus 로고
    • On the existence, uniqueness and convergence of nonlinear mixed finite element methods
    • Chen, Z.: On the existence, uniqueness and convergence of nonlinear mixed finite element methods, Mat. Aplic. Comp. 8 (1989), 241-258.
    • (1989) Mat. Aplic. Comp. , vol.8 , pp. 241-258
    • Chen, Z.1
  • 8
    • 0029697285 scopus 로고    scopus 로고
    • Equivalence between and multigrid algorithms for nonconforming and mixed methods for second order elliptic problems
    • Chen, Z.: Equivalence between and multigrid algorithms for nonconforming and mixed methods for second order elliptic problems, East-West J. Numer. Math. 4 (1996), 1-33.
    • (1996) East-West J. Numer. Math. , vol.4 , pp. 1-33
    • Chen, Z.1
  • 9
    • 2342484838 scopus 로고
    • Modelling of compositional flow in naturally fractured reservoirs
    • Environmental Studies: Mathematical, Computational, and Statistical Analysis, Wheeler, M. F. (ed.), Springer-Verlag, Berlin, New York
    • Chen, Z. and Douglas, J. Jr.: Modelling of compositional flow in naturally fractured reservoirs, Environmental Studies: Mathematical, Computational, and Statistical Analysis, Wheeler, M. F. (ed.), The IMA Volumes in Mathematics and its Applications 79, Springer-Verlag, Berlin, New York, 1995, pp. 65-96.
    • (1995) The IMA Volumes in Mathematics and Its Applications , vol.79 , pp. 65-96
    • Chen, Z.1    Douglas Jr., J.2
  • 10
    • 0001219272 scopus 로고
    • Continuous-time finite element analysis of multiphase flow in groundwater hydrology
    • Chen, Z., Espedal, M. and Ewing, R.: Continuous-time finite element analysis of multiphase flow in groundwater hydrology, Appl. Math. 40 (1995), 203-226.
    • (1995) Appl. Math. , vol.40 , pp. 203-226
    • Chen, Z.1    Espedal, M.2    Ewing, R.3
  • 11
    • 0000761187 scopus 로고    scopus 로고
    • Fully-discrete finite element analysis of multiphase flow in groundwater hydrology
    • to appear
    • Chen, Z. and Ewing, R.: Fully-discrete finite element analysis of multiphase flow in groundwater hydrology, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Chen, Z.1    Ewing, R.2
  • 12
    • 2342635617 scopus 로고    scopus 로고
    • Comparison of various formulations for three-phase flow in porous media
    • to appear
    • Chen, Z. and Ewing, R.: Comparison of various formulations for three-phase flow in porous media, J. Comp. Physics, to appear.
    • J. Comp. Physics
    • Chen, Z.1    Ewing, R.2
  • 13
    • 0002423691 scopus 로고
    • Multiphase flow simulation with various boundary conditions
    • A. Peters et al. (eds.), Kluwer Academic Publishers, Netherlands
    • Chen, Z., Ewing, R. and Espedal, M.: Multiphase flow simulation with various boundary conditions in: A. Peters et al. (eds.), Numerical Methods in Water Resources, Vol. 2, Kluwer Academic Publishers, Netherlands, 1994, pp. 925-932.
    • (1994) Numerical Methods in Water Resources , vol.2 , pp. 925-932
    • Chen, Z.1    Ewing, R.2    Espedal, M.3
  • 14
    • 0000060649 scopus 로고    scopus 로고
    • Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?
    • Comment on by R. Mose, P. Siegel, P. Acker and G. Chavent
    • Cordes, C. and Kinzelbach W.: Comment on 'Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?' by R. Mose, P. Siegel, P. Acker and G. Chavent: Water Resour. Res. 32 (1999), 1905-1909.
    • (1999) Water Resour. Res. , vol.32 , pp. 1905-1909
    • Cordes, C.1    Kinzelbach, W.2
  • 16
    • 0002361227 scopus 로고
    • Comparison of the three-phase oil relative permeability models
    • Delshad, M. and Pope, G. A.: Comparison of the three-phase oil relative permeability models, Transport in Porous Media 4 (1989), 59-83.
    • (1989) Transport in Porous Media , vol.4 , pp. 59-83
    • Delshad, M.1    Pope, G.A.2
  • 17
    • 0002329650 scopus 로고
    • The approximation of the pressure by a mixed method in the simulation of miscible displacement
    • Douglas, J., Ewing, R. and Wheeler, M.: The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Anal. Numér. 17 (1983), 17-33.
    • (1983) RAIRO Anal. Numér. , vol.17 , pp. 17-33
    • Douglas, J.1    Ewing, R.2    Wheeler, M.3
  • 18
    • 84966200192 scopus 로고
    • Numerical methods for a model for compressible miscible, displacement in porous media
    • Douglas, J. Jr. and Roberts, J.: Numerical methods for a model for compressible miscible, displacement in porous media, Math. Comp. 41 (1983), 441-459.
    • (1983) Math. Comp. , vol.41 , pp. 441-459
    • Douglas Jr., J.1    Roberts, J.2
  • 19
    • 0001235787 scopus 로고
    • Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • Douglas, J. Jr. and Russell, T.: Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19 (1982), 871-885.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 871-885
    • Douglas Jr., J.1    Russell, T.2
  • 20
    • 0028741633 scopus 로고
    • Inexact and preconditioned Uzawa algorithms for saddle point problems
    • Elman, H. and Golub, G.: Inexact and preconditioned Uzawa algorithms for saddle point problems, SIAM J. Numer. Anal. 31 (1994), 1645-1661.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1645-1661
    • Elman, H.1    Golub, G.2
  • 21
    • 0003215404 scopus 로고
    • Problems arising in the modeling of processes for hydrocarbon recovery
    • R. Ewing (ed.), SIAM, Philadelphia
    • Ewing, R.: Problems arising in the modeling of processes for hydrocarbon recovery, in: R. Ewing (ed.), The Mathematics of Reservoir Simulation, SIAM, Philadelphia, 1983, pp. 3-34.
    • (1983) The Mathematics of Reservoir Simulation , pp. 3-34
    • Ewing, R.1
  • 22
    • 0026203036 scopus 로고
    • Superconvergence of the velocity along the Gauss lines in mixed finite element methods
    • Ewing, R., Lazarov, R. and Wang, J.: Superconvergence of the velocity along the Gauss lines in mixed finite element methods, SIAM J. Numer. Anal. 28 (1991), 1015-1029.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1015-1029
    • Ewing, R.1    Lazarov, R.2    Wang, J.3
  • 25
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Springer, Berlin
    • Raviart, P. A. and Thomas, J. M.: A mixed finite element method for second order elliptic problems, Lecture Notes in Math. 606, Springer, Berlin, 1977, pp. 292-315.
    • (1977) Lecture Notes in Math. , vol.606 , pp. 292-315
    • Raviart, P.A.1    Thomas, J.M.2
  • 26
    • 0002650114 scopus 로고
    • Finite element and finite difference methods for continuous flows in porous media
    • R. Ewing (ed.), The Mathematics of Reservoir Simulation, Soc. for Industrial Appl. Math., Philadelphia
    • Russell, T. and Wheeler, M.: Finite element and finite difference methods for continuous flows in porous media, in: R. Ewing (ed.), The Mathematics of Reservoir Simulation, Frontiers in Applied Mathematics 1, Soc. for Industrial Appl. Math., Philadelphia, 1983, pp. 35-106.
    • (1983) Frontiers in Applied Mathematics , vol.1 , pp. 35-106
    • Russell, T.1    Wheeler, M.2
  • 27
    • 0015672971 scopus 로고
    • Estimation of three-phase relative permeability and residual oil data
    • Stone, H. L.: Estimation of three-phase relative permeability and residual oil data, J. Canad. Pet. Tech. 12 (1973), 53-67.
    • (1973) J. Canad. Pet. Tech. , vol.12 , pp. 53-67
    • Stone, H.L.1
  • 28
    • 0001669414 scopus 로고
    • On convergence of block-centered finite-differences for elliptic problems
    • Weiser, A. and Wheeler, M.: On convergence of block-centered finite-differences for elliptic problems, SIAM J. Numer. Anal. 25 (1988), 351-375.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 351-375
    • Weiser, A.1    Wheeler, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.