I’d like to draw your attention to some interactive web tools that I’ve built designed to provide beginning students of Partial Differential Equations to explore some elementary examples in two dimensions. In addition to its use in the teaching of PDEs, folks on this forum might be interested because the backend is a Python program written with NGSolve.
I’m currently using these tools in an undergraduate course in PDEs that I teach so students working at an introductory level with little to no programming experience are really the intended audience. The tools mostly involve two-dimensional heat flow at the moment, though there is one fun example that illustrates vibrational eigenmodes. In principle, any PDE specified by a few parameters could be explored using this technique.
The interface is not programmatic. Rather the user specifies a two-dimensional domain via CSG. They can then refine the domain and indicate any Dirichlet type boundary conditions and other parameters via a point and click interface. Once ready, they hit the “solve” button and (if all goes well) an interactive visualization of the solution should appear.
There are several of these linked from our class web page. You can find a
link to that page with the specific links highlighted here.