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An Abridged History of Cell Discretization

  • John Greenstadt
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 11)

Abstract

This brief account will call attention to a line of research which stretches over 40 years, and which appears now to be joining the mainstream of work on the discretization of linear partial differential equations. The first in a series of papers [1] describing the Method of Cells, now called the Cell Discretization Algorithm (CD or CDA), was published in 1959.

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References

  1. 1.
    J. Greenstadt, “On the reduction of continuous problems to discrete form”, IBM Jour. Res. Dev., vol. 3, pp. 355–363 (1959)MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Greenstadt, “Cell discretization I - variational basis”, IBM New York Sci. Ctr. Report (1967)Google Scholar
  3. 3.
    J. Greenstadt, “Cell discretization” in Conference on Applications of Numerical Analysis, Dundee, Scotland, ed. J. Ll. Morris, Springer-Verlag (1971)Google Scholar
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    J. Greenstadt, “Some numerical tests of cell discretization”, IBM Palo Alto Sci. Ctr. Report (1972)Google Scholar
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    P.A. Raviart, J.M. Thomas, “Primal hybrid finite element methods for second-order elliptic equations”, Math. Comp., 31 (138) Rpp. 391–413 (1977)Google Scholar
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    M.R. Dorr, “On the discretization of interdomain coupling in elliptic boundary value problems”, in: Domain Decomposition Methods, Eds., T.F. Chan, R. Glowinski, J. Periaux, O.B. Widlund, SIAM, Philadelphia, PA 1989Google Scholar
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    J. Greenstadt, “ Solution of elliptic systems of partial differential equations by cell discretization”, SIAM J. Sci. Stat. Comput., 14, pp. 627–653 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
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    J. Greenstadt, “The removal of overshoot in P.D.E. solutions by the use of special basis functions”, Computer Meth. in Appl. Mech. and Eng., (1994)Google Scholar
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    J. Greenstadt, “The application of the cell discretization method to time-dependent problems”, Computer Meth. in Appl. Math. and Engineering, (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • John Greenstadt
    • 1
  1. 1.NASA-Ames Research CenterUSA

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