Skip to main content

On the Numerical Treatment of Partial Differential Equations in the Neighborhood of Isolated Singularities with Applications

  • Chapter
Numerische Behandlung von Differentialgleichungen

Abstract

Problems arising in pumping fluids from the ground are treated. Several of the problems are formulated in detail, existence and uniqueness questions are discussed and numerical methods for solving the relevant problems are given.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aronson, D.G. Regularity properties of flows through porous media. SIAM J. on Applied Math. 17 (1969), 461–467.

    Article  Google Scholar 

  2. Aronson, D.G.: Regularity properties of flows through porous media: the interface. Arch. Rat. Mech. Anal. 37 (1970), 1–10

    Article  Google Scholar 

  3. Friedman, A.: Partial differential equations of parabolic type. Prentice-Hall, Englewood Cliffs, New Jersey, 1964.

    Google Scholar 

  4. Fucks, W., Guenther, R.B., Roetman, E.L.: Equations of motion and continuity for fluid flow in a porous medium, Acta Mechanics 12 (1971), 121–129.

    Article  Google Scholar 

  5. Guenther, R.B.: Representations theorems for linear second-order parabolic partial differential equations. J. of Math. Anal. and Appl. 17(1967), 488–5o1.

    Google Scholar 

  6. Guenther, R.B.: Ober die numerische Behandlung gewisser Probleme in der Theorie der Strömungen in einem porösen Medium. Num. Methoden der Approximationstheorie. Bd. 1. Birkhäuser Verlag. ISNM (1971), 41–48.

    Google Scholar 

  7. Guenther, R.B., Roetman, E.L.: Newton-Cotes formulae in n-dimensions. Numer. Math. 14 (1970), 330–345.

    Article  Google Scholar 

  8. Hubbert, M.K.: Darcy’s law and the field equations of the flow of underground fluids. AIME Pet. Trans. 8 (1956), 222–239.

    Google Scholar 

  9. Muskat, M.: The flow of homogeneous fluids through porous media. 2nd. printing. Ann Arbor: Edwards, 1946.

    Google Scholar 

  10. Oleinik, O.A., Kalashnikov, A.S., Chzou Yui-Lin: The Cauchy problem and boundary value problems for equations of the type of nonstationary filtration. Izvestija Akad. Nauk SSSR, ser. mat. 22 (1958), 667–704.

    Google Scholar 

  11. Polubarinova-Kochina, P.Ya.: Theory of ground water movement. Princeton, New Jersey: Princeton University Press. 1962. (Translation from the Russian original published in 1952 in Moscow).

    Google Scholar 

  12. Scheidegger, A.E.: Hydrodynamics in porous media. Handbuch der Physik, VIII/2. Berlin-GöttingenHeidelberg. Springer-Verlag (1959), 625–662.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer Basel AG

About this chapter

Cite this chapter

Guenther, R.B. (1975). On the Numerical Treatment of Partial Differential Equations in the Neighborhood of Isolated Singularities with Applications. In: Numerische Behandlung von Differentialgleichungen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 27. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5532-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5532-7_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5533-4

  • Online ISBN: 978-3-0348-5532-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics