# A Gentle Introduction to the Finite Element Method

Almost every engineer today have some knowledge of theoretical and practical aspects of FEM. And many have played with various software packages at some point of time.

Well that is enough if you just want to perform analysis but if you want to truly understand the mathematical aspects of FEM and want to get a feel of the numerical methods under the hood of FEM then this short lecture is for you.

Here’s the introduction, plucked straight from the course. IF you like it, you will enjoy the lecture.

The course is divided into five lessons and all this in 100 pages. Happy Learning!!

If you haven’t been hiding under a stone during your studies of engineering, mathematics or physics, it is very likely that you have already heard about the Finite Element Method. Maybe you even know some theoretical and practical aspects and have played a bit with some FEM software package. What you are going to find here is a detailed and mathematically biased introduction to several aspects of the Finite Element Method.

This is not however a course on the Analysis of the method. It is just a demonstration of how it works, written as applied mathematicians usually write it. There is going to be mathematics involved, but not lists of theorems and proofs. We are also going from the most particular cases towards useful generalizations, from example to theory.

It is going to be one hundred pages with many figures and many ideas repeated over and over, so that you can read it with ease. These notes have evolved during the decade I have been teaching finite elements to mixed audiences of mathematicians, physicists and engineers. The tone is definitely colloquial. I could just claim that these are my classnotes and that’s what I’m like.

There’s much more than that. First, I believe in doing your best at being entertaining when teaching. At least that’s what I try. Behind that there is
a deeper philosophical point: take your work (and your life) seriously but, please, don’t take yourself too seriously.

I also believe that people should be duly introduced when they meet. All this naming
old time mathematicians and scientists only by their last names looks to me too much
like the Army. Or worse, high school!

I think you have already been properly introduced to the great Leonhard Euler, David Hilbert, Carl Friedrich Gauss, Pierre Simon Laplace and George Green. If you haven’t so far, consider it done here. This is not about history.

It’s just good manners. Do you see what I mean by being colloquial?

Anyway, this is not about having fun, but since we are at it, let us try to have a good time while learning. If you take your time to read these notes with care and try the exercises at the end of each lesson, I can assure that you will have made a significant step in your scientific persona. Enjoy!

Click the below link to access the excellent PDF. Don’t forget to thanks to Francisco Jaview Sayas !

A gentle introduction to the Finite Element Method by Francisco–Javier Sayas