Semi-discrete finite difference multiscale scheme for a concrete corrosion model: a priori estimates and convergence

We study a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction–diffusion equations coupled with an ordinary differential equation. We prove energy and regularity estimates and use them to get the necessary compactness of the approximate solutions. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the solution to our system.