  This paper addresses the topological structure of steady, anisotropic,
inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b)
direct formulations are discussed. Differential operators are represented by
sparse incidence matrices, while weighted mass matrices play the role of
metric-dependent Hodge matrices. The resulting mixed formulations are
point-wise divergence-free if the right hand side function f = 0. The method is
inf-sup stable and displays optimal convergence on orthogonal and non-affine
grids.
