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

Abstract

AbstractWe 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).