DOF reported (somewhat) misleading (IMO)

[DanielDoehring]

I think that the current definition (and report) of the DOF is confusing, if not misleading.
I would expect that DOF measures the total number of DG coefficients, i.e., the size of the semidiscretization.
However, as it is currently implement, the DOF per field are reported:

Trixi.jl/src/solvers/dg.jl

Lines 409 to 411 in 00292d1

	@inline function ndofs(mesh::MeshesDGSEM, dg::DG, cache)
	nelements(cache.elements) * nnodes(dg)^ndims(mesh)
	end

I suggest that we either multiply the value DOF with nvariables(equaitons) or write in the report

Trixi.jl/src/semidiscretization/semidiscretization_hyperbolic.jl

Line 246 in 00292d1

summary_line(io, "total #DOFs", ndofs(semi))

total #DOFs per field.

[ranocha]

As far as I can tell, our current way of reporting the DOF is used quite a lot in the literature. This doesn't mean that adding a hint wouldn't be nice

[andrewwinters5000]

Yeah, it is relatively standard (at least in the turbulence community) that the reported number of DOFs is given per equation, although I am not opposed to having both reported.