Lets do a short dive into the history of the finite element method. I will use just one paper (its cheating I know), appropriately named “A BRIEF HISTORY OF THE BEGINNING OF THE FINITE ELEMENT METHOD”. Thread. https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819961130%2939%3A22%3C3761%3A%3AAID-NME22%3E3.0.CO%3B2-5

The paper traces the history to 5 specific groups of papers and then discusses each of them. We start with Courant. If the name seems familiar, it should be. He is the C of the famous CFL condition, which is applicable every time a wave like equation is solved.

He used triangles to discretize, and FEM has been associated with triangles ever since. In a review of the paper, another author notes about it “Flares of brilliance are interwoven with expanses of flat material”. Such statements on academic paper are (sadly) rare.

The next author to have a significant effect is Argyris. An interesting bit is that the paper was published in Aircraft Engineering and Aerospace Technology. Applications to aircrafts have historically been a driver to push numerical methods forward.

He developed the concept of representing the discretization using matrices, something we are all too familiar with today. Interestingly, he uses quadrilaterals instead of triangles.

Then we move on to RJ Turner, continuing our association with aircrafts. Turner worked for Boeing. He also starts with using quadrilaterals but then makes a very important statement. Today it may seem simple, but for the time this would have been a significant development.

Next, we have Clough, who, in keeping with our association with Aircrafts and especially Boeing, charts the history of developments of this method at Boeing, but perhaps significantly invents the name “Finite Element Method”.

It is crucial to note that until now, all developments are specifically for structural problems. We are always aware, although maybe unconsciously, of this because of the naming of the matrices. They are always mass matrix, or stiffness matrix.

We can thank the final authors Zienkiewicz and
Cheung for using it for non-structural applications. They used it for heat transfer and also discussed concepts we take for granted today, the sparsity of the matrices.

Zienkiewicz also later wrote a book whose length is something to behold.

And thus ends this thread. FEM today is used in so many areas. We have these authors and significantly more to thank for this.