Improve documentation of the analysis callback

[ranocha]

@Alexander-Barth Does this address your comment in #264 sufficiently?

[JoshuaLampert]

LGTM! Thanks!

[Alexander-Barth]

Can you quantify the "growth one would obtain from a standard spatial discretization that does not conserve these invariants" ? Just of the order of magnitude for this test case might be sufficient.

Or maybe it is easier to provide the initial total entropy? So that the reader can see that an increase of 0.005 corresponds to an increase of 10% or rather 0.0001% ...

[ranocha]

Can you quantify the "growth one would obtain from a standard spatial discretization that does not conserve these invariants" ? Just of the order of magnitude for this test case might be sufficient.

Or maybe it is easier to provide the initial total entropy? So that the reader can see that an increase of 0.005 corresponds to an increase of 10% or rather 0.0001% ...

That's a good suggestion, thanks. I added this information on the relative change (which is of the order $10^{-6}$ in this case).

[JoshuaLampert]

Great, thanks again!

[JoshuaLampert]

Is this resolved from your perspective after merging this PR, @Alexander-Barth? You can see the preview of the documentation here: https://numericalmathematics.github.io/DispersiveShallowWater.jl/previews/PR266/callbacks/#Analysis-Callback.

[Alexander-Barth]

Yes, perfect! This is exactly the type of information behind my question.