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

TL;DR

This paper introduces a semi-discrete finite difference multiscale scheme for modeling concrete corrosion, providing theoretical approximation estimates and convergence analysis, supported by numerical simulations.

Contribution

The work develops a novel multiscale finite difference scheme for a concrete corrosion model, with rigorous proof of energy estimates and convergence, and demonstrates its effectiveness through numerical experiments.

Findings

Energy and regularity estimates established

Convergence of the scheme proven

Numerical simulations illustrate the model's behavior

Abstract

We propose 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 ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.