  In this paper, we discuss the accuracy and the robustness of the mixed
Virtual Element Methods when dealing with highly-anisotropic diffusion
problems. In particular, we analyze the performances of different approaches
which are characterized by different sets of both boundary and internal degrees
of freedom in presence of a strong anisotropy of the diffusion tensor with
constant or variable coefficients. A new definition of the boundary degrees of
freedom is also proposed and tested.
