  An implicit Euler finite-volume scheme for a parabolic reaction-diffusion
system modeling biofilm growth is analyzed and implemented. The system consists
of a degenerate-singular diffusion equation for the biomass fraction, which is
coupled to a diffusion equation for the nutrient concentration, and it is
solved in a bounded domain with Dirichlet boundary conditions. By transforming
the biomass fraction to an entropy-type variable, it is shown that the
numerical scheme preserves the lower and upper bounds of the biomass fraction.
The existence and uniqueness of a discrete solution and the convergence of the
scheme are proved. Numerical experiments in one and two space dimensions
illustrate, respectively, the rate of convergence in space of our scheme and
the temporal evolution of the biomass fraction and the nutrient concentration.
