In this paper, the numerical approximation of a nonlinear diffusion equation arising in contaminant transport is studied. The equation is characterized by advection, diffusion, and adsorption. Assuming the adsorption term is modeled by a Freundlich isotherm, it can be nonlinear in concentration and nondifferentiable as the concentration approaches zero. We consider the approximation of this equation by a method which upwinds the advection and incorporates diffusion using a mixed finite element method. Error estimates for a semi-discrete formulation are derived, and numerical results for a fully discrete formulation are given.