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

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.

arXiv comment22 pages, 1 figure, submitted to Japan Journal of Industrial and Applied Mathematics

References in corpus (2)

• Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition
• Homogenization of a locally-periodic medium with areas of low and high diffusivity

Cited by in corpus (1)

• A semidiscrete Galerkin scheme for a coupled two-scale elliptic-parabolic system: well-posedness and convergence approximation rates