An Introduction to a Compatible Spectral Discretization Method

In this article, I try to explain what one means when one refers to 'compatible' or 'mimetic' discretization methods. I will show why this approach is so appealing from a computational and physical point of view. In this respect, this is not really a scientific paper, although some new ideas will be presented, but-as the title suggests-an introduction to a new way of looking at discretization methods. This article shows the path from physical modeling, to a representation in terms of differential forms, algebraic topological cochains with an implementation in terms of an orthogonal polynomial.