Uncaught Exception from the no-flux steady-state diffusion example

[guyer]

Discussed in #951

^{Originally posted by CalebDmArcher September 18, 2023}
I am trying the last example from examples/diffusion/mesh1D.py which is the "Fully implicit solutions are not without their pitfalls, particularly in steady state..." section.

The code of the steady-state part got the error "RuntimeError: Factor is exactly singular" which comes from the code DiffusionTerm(coeff=D).solve(var=phi). Is it because the latest version of the library can catch and raise exceptions for the cases where there can be more than one solution for the PDE?

[guyer]

Some solvers, e.g., PETSc, are willing to return one of the infinite possible solutions.
Others, e.g., SciPy, raise an exception.

The example should be more robust.

[guyer]

Fixed by #1015