Skip to main content
SpringerLink
Log in

Finite element approximations of two-phase miscible incompressible displacement with discontinuous coefficients

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

Two-phase, miscible, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. Many numerical methods have been given by different authors to this system, but these methods need very high regularity conditions. Actually, in most practical applications these regularity conditions couldn’t be satisfied. In this paper, the problem of discontinuous coefficients with lower regularity conditions is considered and the error estimates are demonstrated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Feistauer, M. and Veronika Sobtikova, Finite element approximation of nolinear elliptic problems with discontinuous coefficients, RAIRO Numer. Anal., 1990,24:457–500.

    MATH  Google Scholar 

  2. Ewing, Richard E., Wheeler, M. F., Galerkin methods for miscible displacement problems in porous media, SIAM J. Numer. Anal., 1980,17:351–365.

    Article  MATH  Google Scholar 

  3. Feistauer, M., Zenisek, A., Finite element solution of nolinear elliptic problems, Numer. Math., 1988,52:147–163.

    Article  MATH  Google Scholar 

  4. Feistauer, M., On the finite element approximation of a cascade flow problems, Numer. Math., 1987, 50:655–684.

    Article  MATH  Google Scholar 

  5. Cialet, P. G., The Finite Element Method for Elliptic Problems, Amsterdam, North-Holland, 1978.

    Google Scholar 

  6. Adames, R. A., Soblev Space, Academic Press, New York, 1975.

    Google Scholar 

  7. Douglas, Jim, Jr, Wheeler, M. F., The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Numer. Anal. 1983,17:17–33.

    MATH  Google Scholar 

  8. Lin Qun, Zhu Qiding, The Preprocessing and Postporocessing for the Finite Element Method, Shanghai Scientific and Technical Publisher, 1994, (in Chinese)

  9. Chen Chuanmiao, Huang Yunqing, High Accuracy Theory of Finite Element Method, Human Scientific and Technical Publisher, Changsha, 1995. (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Math., Shandong Univ., 250100, Jinan

    Sun Wentao & Liu Yunxian

Authors
  1. Sun Wentao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liu Yunxian
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by both the National (19871051) and Shandong Province Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wentao, S., Yunxian, L. Finite element approximations of two-phase miscible incompressible displacement with discontinuous coefficients. Appl. Math. Chin. Univ. 14, 451–460 (1999). https://doi.org/10.1007/s11766-999-0075-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-999-0075-1

1991 MR Subject Classification

Keywords

Search

Navigation