Appropriate numerical algorithms are requested for dealing with suchkind of problems. We focus here on the particular case of a scalarmodel that can be formulated in a fixed domain. To overcome thedifficulties that are due to the degeneracy, we first perturb theoriginal model and end up with a regular parabolic one. For theresulting we employ standard discretization methods (implicit in timeand an upwinded box scheme in space) and show that these lead tostable and convergent algorithms. A few words will be said on how tosolve the time discrete nonlinear problems.