Sounds perfectly normal :)
The standard advice here at work for one of our modelling packages is: if it crashes try rotating your input model by one degree and try again. Most of the time that will fix it. If it doesn't fix it try one degree in the other direction.
Is correctness somehow assured provided it doesn't crash? Or is the whole thing just a joke?
I'm sure lots of people do. We're a commercial company selling consultancy service around this software (technically around some inhouse tools built on top of this software), among many other things.
Is correctness somehow assured provided it doesn't crash?
On the whole well tested PDE solvers either crash, give answers that are off by several orders of magnitude, or give a correct answer. (If the answer they give is relevant to what you're trying to model is left as an exercise to the reader)
We're reasonably sure that, if the calculations converge, the solution provided is a correct numeric approximation (within the error bounds given) of the PDEs we're claiming to solve. We also believe that the PDEs we're using provide a reasonable balance between modeling what we claim we're modelling and our computation running in a reasonable amount of time.