Yeah it'd be cool to consider this approach for some other domains. Sometime soon I'll make it so you can change the word in the top-left from "INVOICE" to "QUOTE" or "RECEIPT". The nice thing about an invoice is you know there's going to be a relatively small amount of data, so storing the state in the URL is a plausible approach (even if it looks obscene to discerning users ).
Predicting how things evolve in space-time is a fundamental need. Finite element methods deserve the glory of a place at the top of the HN list. I opted for "orthogonal collocation" as the method of choice for my model back in the day because it was faster and more fitting to the problem at hand. A couple of my fellow researchers did use FEM. It was all the rage in the 90s for sure.