In this paper, the authors consider a parametrized non-linear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite volume discretization leads to a high-dimensional discrete non-linear problem so that simulation of the parametrized problem for various different parameters is very costly. Therefore, the reduced-basis method is applied, so that the number of degrees of freedom is reduced significantly and a fast numerical simulation of the model is possible. To control the error, an a-posteriori error estimator is derived. Numerical experiments show the efficiency of the approach.@en