I think there will probably be some interplay between physical effects (due to the
abrupt interface between two materials with different effective masses)
and artificial effects (due to the discretization of the model).

It would not surprise me that you get unphysical effects for sufficiently
high energies/short wavelengths ("high" to be defined ;)) because then
you will be probing the differences between the discretization
schemes used.

I would certainly start by using a single discretization scheme and checking that
you get the results you expect. If I understand correctly you are only trying to
use different discretization schemes for performance reasons, so on a practical
level I would also suggest looking at whether the extra hassle of using different
discretization schemes is worth the gain in speed.

Happy Kwanting,