First error bounds for the porous media approximation of the Poisson-Nernst-Planck equations

We study the well-accepted Poisson-Nernst-Planck equations modeling transport of charged particles. By formal multiscale expansions we rederive the porous media formulation obtained by two-scale convergence in [42, 43]. The main result is the derivation of the error which occurs after replacing a highly heterogeneous solid-electrolyte composite by a homogeneous one. The derived estimates show that the approximation errors for both, the ion densities quantified in L2-norm and the electric potential measured in H1-norm, are of order O(s1/2).