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A Galerkin Method for Liquid Pipelines

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Computing Methods in Applied Sciences and Engineering

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((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.

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References

  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.

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  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.

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  3. T.Dupont and L. Wahlbin, L2 optimality of weighted-H1 projections into piece-wise polynomial spaces, to appear.

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  4. Max Gunzburger, private communication.

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  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.

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Author information

Authors and Affiliations

  1. University of Chicago, Chicago, Ill., 60637, USA

    Todd Dupont

  2. Rice University, Houston, Texas, 77001, USA

    H. H. Rachford Jr.

Authors
  1. Todd Dupont
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  2. H. H. Rachford Jr.
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Editor information

Editors and Affiliations

  1. Domaine de Voluceau BP 105, IRIA LABORIA, 78150, Rocquencourt, Le Chesnay, France

    R. Glowinski  & J. L. Lions  & 

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© 1976 Springer-Verlag Berlin Heidelberg

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Dupont, T., Rachford, H.H. (1976). A Galerkin Method for Liquid Pipelines. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering. Lecture Notes in Economics and Mathematical Systems, vol 134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85972-4_19

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  • DOI: https://doi.org/10.1007/978-3-642-85972-4_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07990-3

  • Online ISBN: 978-3-642-85972-4

  • eBook Packages: Springer Book Archive

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