Well, moderately cool for me. I finally finished the code, and was able to get some visualization ready for it. I'm going to do some very complicated geometries next, but for now we'll make do with the unit sphere. The great thing about the finite element method is that it can handle complicated geometries with little to no change in the solver code, in my case I won't have to change a single thing, all I have to do is input the mesh.
Here is what the mesh generator gave me for the unit sphere, (chopped in half)
and here is another picture of the same sphere
The way I visualized the solution was by taking a cross section and moving it through the domain, having the cross section take on colors associated with the functional values. Here's the video for that
17 hours ago