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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Greenstadt, “On the reduction of continuous problems to discrete form”, IBM Jour. Res. Dev., vol. 3, pp. 355–363 (1959)
J. Greenstadt, “Cell discretization I - variational basis”, IBM New York Sci. Ctr. Report (1967)
J. Greenstadt, “Cell discretization” in Conference on Applications of Numerical Analysis, Dundee, Scotland, ed. J. Ll. Morris, Springer-Verlag (1971)
J. Greenstadt, “Some numerical tests of cell discretization”, IBM Palo Alto Sci. Ctr. Report (1972)
P.A. Raviart, J.M. Thomas, “Primal hybrid finite element methods for second-order elliptic equations”, Math. Comp., 31 (138) Rpp. 391–413 (1977)
J. Greenstadt, “The cell discretization algorithm for elliptic partial differential equations”, Siam J. Sci. Stat. Comput., 3, pp. 261–288 (1982)
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 1989
C. Bernardi, Y. Maday & A.T. Patera, “A new nonconforming approach to domain decomposition; the Mortar Element Method”, College de France Seminar, (1990), Pitman, eds., H. Brezis, J.-L. Lions.
J. Greenstadt, “Cell discretization of nonselfadjoint linear elliptic PDE’s”, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 1074–1108.
J. Greenstadt, “ Solution of elliptic systems of partial differential equations by cell discretization”, SIAM J. Sci. Stat. Comput., 14, pp. 627–653 (1993)
H. Swann, “ On the use of Lagrange multipliers in domain decomposition for solving elliptic problems”, Math. of Comp., vol. 60, no. 201, pp. 49–78 (1993)
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)
J. Greenstadt, “The application of the cell discretization method to time-dependent problems”, Computer Meth. in Appl. Math. and Engineering, (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Greenstadt, J. (2000). An Abridged History of Cell Discretization. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-59721-3_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64098-8
Online ISBN: 978-3-642-59721-3
eBook Packages: Springer Book Archive