[Gmsh] edge length * 0.5 => number of elements * 6?

[Geordie McBain]

2013/7/1 Nico Schlömer <nico.schloemer at gmail.com>:
> for a tetrahedral mesh, when scaling the characterstic length by 0.5, I
> notice that the number of tetrahedra roughly increases by a factor of 6.
> Is this generally true? Does anyone know a reference for this?

I would have guessed à priori that the factor was eight (one over the
cube of the length-scaling).  My numerical experiments with the
attached simple cubic geometry aren't conclusive, but the number seems
a bit short of that, though higher than 6.

$ gmsh -3 cube.geo -clscale $CLSCALE | grep elements

CLSCALE elements ratio
1.0              2 289        -
0.5            15 605    6.8
0.25         114 034   7.3
0.125       748 859   6.6
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