Error Bounds on Semi-Discrete Finite Element Approximation of a Moving-Boundary System Arising in Concrete Corrosion

Abstract

Finite element approximations of positive weak solutions to a one-phase unidimensional moving-boundary system with kinetic condition describing the penetration of a sharp-reaction interface in concrete are considered. A priori and a posteriori error estimates for the semi-discrete fields of active concentrations and for the position of the moving interface are obtained. The important feature of the system of partial differential equations is that the nonlinear coupling occurs due to the presence of both the moving boundary and the non-linearities of localized sinks and sources by reaction.