Skip to main content
SpringerLink
Log in

C0 — Collocation — Galerkin methods

  • Conference paper
  • First Online:
Codes for Boundary-Value Problems in Ordinary Differential Equations

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 76))

Abstract

A C0-Collocation-Galerkin (C0-C-G) method is formulated and analyzed for finite element solution of linear and nonlinear singular boundary-value problems. Theoretical error estimates are ascertained for both the linear problems and a specific class of nonlinear problems. Convergence rates and superconvergence behavior are established and verified in numerical experiments. As a particular class of important research applications, we consider heat and mass transfer problems that arise for catalytic reactors in chemical engineering. The Jacobi points are introduced to determine optimal orders of accuracy and utilized in a new method for determining the boundary flux to optimal order. Numerical results are presented for sample problems.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Diaz, "A hybrid collocation Galerkin method for the two-point boundary-value problem using continuous piecewise polynomial spaces," Ph.D. thesis, Rice University, Houston, Texas, 1975.

    Google Scholar 

  2. M.F. Wheeler: "A C0-collocation finite element method for two-point boundary-value problems and one space dimensional parabolic problems," SIAM J. Numer. Anal. Vol. 14, No. 1, 1977.

    Google Scholar 

  3. G.F. Carey and B.A. Finlayson: "Orthogonal collocation on finite elements," J. Chem. Eng. Sci., vol. 30, pp. 587–596, 1975.

    Article  Google Scholar 

  4. M.F. Wheeler and G.F. Carey: "Analysis of collocation-Galerkin methods and Superconvergence for nonlinear two-point problems" (in preparation).

    Google Scholar 

  5. R.D. Russell and L.F. Shampine: "Numerical methods for singular boundary-value problems," SIAM J. Numer. Anal., Vol. 12, No. 1, 1975.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Texas Institute for Computational Mechanics, The University of Texas at Austin, USA

    G. F. Carey

  2. Mathematical Sciences Department, Rice University, USA

    M. F. Wheeler

Authors
  1. G. F. Carey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. F. Wheeler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

B. Childs M. Scott J. W. Daniel E. Denman P. Nelson

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Carey, G.F., Wheeler, M.F. (1979). C0 — Collocation — Galerkin methods. In: Childs, B., Scott, M., Daniel, J.W., Denman, E., Nelson, P. (eds) Codes for Boundary-Value Problems in Ordinary Differential Equations. Lecture Notes in Computer Science, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09554-3_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-09554-3_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09554-5

  • Online ISBN: 978-3-540-34858-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation