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I am interested in the history of Finite Element Methods and Methods of Weighted Residuals (MWR), especially reduced quadrature and collocation methods. I have a paper coming out called “Orthogonal Collocation Revisited” which has a brief section on history of MWR and collocation methods. It’s at: https://authors.elsevier.com/a/1YHLy_12dr4lJw

I have found and read 7 articles on the history of FEM and a few presentations. One paper frequently cited as “a first” is Courant’s 1943 paper (based on 1941 presentation) “Variational Methods for the Solution of Problems of Equilibrium and Vibrations”. It seems the appendix of the paper is responsible for its citation as a first finite element paper. In the appendix he treats a torsion problem, first using a Raleigh-Ritz method with simple one and two term global trial functions. He then checks the results with a finite difference method on grids of triangles. He gives no details of the calculations. He also states:

“…. [the finite difference method] is obviously adaptable to any type of domain. Much more so than the Raleigh-Ritz procedure in which the construction of admissible functions would usually offer decisive obstacles.”

Since he does not use a variational method on grids of triangles and seems to think this would be difficult, why is the paper considered a first paper on the FEM?

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  • $\begingroup$ Probably because it looks close enough superficially, and attaching Courant's name to originating something makes it look more "worthy". $\endgroup$ – Conifold Feb 6 at 21:31

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