Advertisement

A Galerkin Method for Liquid Pipelines

  • Todd Dupont
  • H. H. RachfordJr.
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 134)

Abstract

The flow of a liquid in a pipe is described by a first-order hyperbolic system. This paper provides an a priori error analysis for a Galerkin method for the approximate solution of this system. The continuous-time Galerkin method and a linearized-Crank-Nicolson version of it are treated.

Keywords

Galerkin Method Differential System Homogeneous Linear System Positive Definite Symmetrizer Pipe Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Douglas, Jr., T. Dupont, and L. Wahlbin, Optimal L error estimates for Galerkin approximations to solutions of two point boundary value problems, Math. Comp. 29 (1975), 475–483.MathSciNetMATHGoogle Scholar
  2. 2.
    T.Dupont, Galerkin methods for modeling gas pipelines, Constructive and Computational Methods for Differential and Integral Equations, Lecture Note in Mathematics No. 430, Springer Verlag, 1974, New York.Google Scholar
  3. 3.
    T.Dupont and L. Wahlbin, L2 optimality of weighted-H1 projections into piece-wise polynomial spaces, to appear.Google Scholar
  4. 4.
    Max Gunzburger, private communication.Google Scholar
  5. 5.
    H. H. Rachford, Jr., and E. L. Ramsey, Application of variational methods to model transient flow in complex liquid transmission systems, Society of Petroleum Engineers paper no. SPE 5663, presented September 1975, to appear in SPE Journal.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Todd Dupont
    • 1
  • H. H. RachfordJr.
    • 2
  1. 1.University of ChicagoChicagoUSA
  2. 2.Rice UniversityHoustonUSA

Personalised recommendations