The first part of the process we have to go through to solve partial differential equations on a computer is called discretization, whereby continuously-varying partial derivatives are represented in terms of discrete quantities. This is necessary because a computer can only store an process a finite amount of information, in contrast to the infinite amount which a general, continuous function might represent. A very large number of methods exist of doing this discretization — among them the Finite Volume (FV), Finite Element (FE) and Spectral methods.
We're going to be concentrating on the Finite Difference (FD) method: it is probably the easiest to understand conceptually, and is widely used in glaciology and beyond.
The Lab Classes on Finite Differencing are split up into the following parts: