Basis Functions

What are “basis functions”?

Intuitively, a basis is a collection of simple building blocks that can be (linearly) combined to create something more complicated.

So, if we define $\Phi(x) = 0.3 \sin(x) + 1.6 x + 3$, then one could say that $\Phi$ is a linear combination of the basis functions $\{\sin(x), x, 1\}$

So, what basis functions should I use?

Although we are free to apply the Finite Element Method to just about any set of basis functions, some choices are more practical than others. In particular, there are a few …