  We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck
equation in bounded spatial domains with specular reflection type boundary
conditions. The method of proof involves the construction of a particular class
of test functions to be chosen in the weak formulation of the kinetic model.
This involves the analysis of the underlying Hamiltonian dynamics of the
kinetic equation coupled with the reflection laws at the boundary. This
approach only demands the solution family to be weakly compact in some weighted
Hilbert space rather than the much tricky $\mathrm L^1$ setting.
