Recently, I took a course on numerical methods where we learned about Galerkin's Method of Weighted Residuals. We were told that it forms the basis of the Finite Element Method .
However, in most introductory texts I've seen on FEM, they start with a simple example where they manually write out the equations to minimize the potential energy at each node. For instance, see this example of a system of springs. There are no test functions, so it doesn't seem to be the MWR.
So, my question is:
- Is there a name for this other method?
- What are the practical and numerical differences between it and the Galerkin Method of Weighted Residuals? (e.g., is it easier to set up for certain problems? Does it have better numerical precision or stability?)