Save additional node variables in SaveSolutionCallback

[DanielDoehring]

Save additional stuff in the solution callback for convenient visualization.

[github-actions]

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[DanielDoehring]

Currently, the PR is somewhat inconsistent as for hyperbolic equations there is a dispatch based on the volume integral type, and for the parabolic equations we use an if-clause. This should be unified IMO.

[bennibolm]

In general, this looks good to me. Unfortunately, the correct export of the "limiting coefficient" is not CI tested extensively.
But, if you tested it locally and say it works properly, I'm fine with merging this after the one issue.

[DanielDoehring]

Maybe it also makes sense to add new functions get_derived_solution_variables ?

[DanielDoehring]

@JoshuaLampert could you maybe also take a look and leave your thoughts here?

[JoshuaLampert]

Thanks! I can image, this is a very useful feature. However, I would like to discuss the interface first, see my comment below.

[DanielDoehring]

I generalized the implementation such that now users can supply their own functions to be stored in the solution file.

I need to test the mpi-implementations, but from my side this is ready for review.

[JoshuaLampert]

Thanks! I left two comments about documentation below.

[JoshuaLampert]

LGTM!

[bennibolm]

Thanks a lot!

[JoshuaLampert]

I have converted it to a draft so it's not accidentally merged because this is breaking.

[ranocha]

Could you please merge main into your branch and resolve the conflicts so that we can prepare the breaking release? Please ping me afterwards.

[DanielDoehring]

Ready to go @ranocha !

[ranocha]

Thanks