  In this work we consider an extension of a recently proposed structure
preserving numerical scheme for nonlinear Fokker-Planck-type equations to the
case of nonconstant full diffusion matrices. While in existing works the
schemes are formulated in a one-dimensional setting, here we consider
exclusively the two-dimensional case. We prove that the proposed schemes
preserve fundamental structural properties like nonnegativity of the solution
without restriction on the size of the mesh and entropy dissipation. Moreover,
all the methods presented here are at least second order accurate in the
transient regimes and arbitrarily high order for large times in the hypothesis
in which the flux vanishes at the stationary state. Suitable numerical tests
will confirm the theoretical results.
