The number of coupling iterations is an ill-conditioned observable and therefore sometimes system dependent. We went through the same pain with an integration test in preCICE. I recommend to not check for this number.

If yes, how much additional complexity do we get here? How much code duplication does this introduce? Currently the systemtests repository bundles certain functionality for several tests (result comparison, docker). Do we need this functionality here?

Let's keep this as minimal as possible. Let's not test things that are already tested in preCICE tests. What we want to test here is the FEniCS adapter. You already have the check against the analytical solution. So the result comparison is not needed in my opinion.

I did not know that the coupling iterations are that sensitive. From my personal experience checking the number of iterations was quite useful in the past. Here it allowed us to uncover a bugs, if I remember correctly: If initialization is buggy, this often increases the number of iterations, but does not break the code. Without checking the iterations we wouldn't have uncovered this bug. I think I came across a similar situation for my research on waveform iteration, as well.

Therefore, I would like to keep this check. But I agree: One should also not look too closely, especially, if the iterations are system dependent.