For a given 3D domain, two unstructured tetrahedral meshes M_1 and M_2 are generated. The average edge length in M_1 is double the average edge length of M_2.
Are there estimates on the ratio of the number of tetrahedra in both meshes?
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If the edge lengths decrease by a factor $k$, the number of tetrahedra will typically increase by between $k^2$ and $k^3$ depending on the adaptivity of the mesh. A purely uniform mesh will see $k^3$, just as a uniform grid of length $1/n$ has $O(n^3)$ cells. A highly adaptive mesh with full resolution near a surface will increase by roughly $k^2$, since most of the elements will occur in a band near the surface. It is also possible to see only a $k$ factor increase if the refinement is near a curve, but this is less common.