  This paper is devoted to the numerical resolution of an anisotropic
non-linear diffusion problem involving a small parameter \varepsilon, defined
as the anisotropy strength reciprocal. In this work, the anisotropy is carried
by a variable vector function b. The equation being supplemented with Neumann
boundary conditions, the limit \varepsilon \infty 0 is demonstrated to be a
singular perturbation of the original diffusion equation. To address
efficiently this problem, an Asymptotic-Preserving scheme is derived. This
numerical method does not require the use of coordinates adapted to the
anisotropy direction and exhibits an accuracy as well as a computational cost
independent of the anisotropy strength.
