A gentle introduction to the Finite Element Method

If you haven’t been hiding under a stone during your studies of engineering, mathemat-ics 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. An aspect where this course differs from most of the many introductory books on finite elements is the fact that I am going to begin directly with the two–dimensional case. I’ve just sketched the one dimensional case in an appendix. Many people think that the one–dimensional case is a better way of introducing the method, but I have an inner feeling that the method losses richness in that very simple situation, so I prefer going directly to the plane