The finite-element method, Part I: R. L. Courant [Historical Corner]

@article{Pelosi2007TheFM,
  title={The finite-element method, Part I: R. L. Courant [Historical Corner]},
  author={G. Pelosi},
  journal={IEEE Antennas and Propagation Magazine},
  year={2007},
  volume={49},
  pages={180-182}
}
  • G. Pelosi
  • Published 2007
  • Mathematics
  • IEEE Antennas and Propagation Magazine
This paper focused on finite elements. Also contains a brief biography of Richard L. Courant, the father of finite elements. The finite-element method, in its presently accepted forms, can be credited to no lesser a person than Richard L. Courant. Using piecewise-linear approximants on a set of triangles, which he called "elements," he dashed off a few two-dimensional examples - and the finite-element method was born. 

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References

SHOWING 1-8 OF 8 REFERENCES
Application of finite elements to the solution of Helmholtz's equation
A novel method, that of finite elements, for the solution of Helmholtz's equation is suggested. Various 2- and 3-dimensional problems are solved using this method, and the results are compared withExpand
Numerical Solution of Dielectric Loaded Waveguides: I-Finite-Element Analysis
A variational expression of the electromagnetic fields in dielectric loaded waveguides is derived. This expression is discretized using the finite-element method and an electromagnetic couplingExpand
Variational methods for the solution of problems of equilibrium and vibrations
As Henri Poincare once remarked, "solution of a mathematical problem" is a phrase of indefinite meaning. Pure mathematicians sometimes are satisfied with showing that the non-existence of a solutionExpand
Finite element solution of waveguide problems
TLDR
The solution of Helmhohz's equation in regions of arbitrary cross-section is obtained by the finite element method. Expand
EM Programmer's notebook - General chair's report on the 8th International Workshop on Finite Elements for Microwave Engineering, Stellenbosch, South Africa, May 2006
  • D. Davidson
  • Engineering
  • IEEE Antennas and Propagation Magazine
  • 2006
[DBD] This is also the last EM Programmer's Notebook that John will be co-editing. With great foresight, John initiated the first column in the October, 1992, issue, and it has gone from strength toExpand
The hypercircle in mathematical physics
Bahrani , and 0 . C . Zienkiewicz , " Application of Finite Elements to the Solution of Helmholtz ' s Equation Numerical Solution of Dielectric Loaded Waveguides . I - Finite - Element Analysis
  • Alta Frequenza
  • 1969
Distributed and Lumped Networks