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Semi-discrete finite difference multiscale scheme for a concrete corrosion model: a priori estimates and convergence. (English) Zbl 1457.65043

Summary: 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure

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References:

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