Convergence of a Finite Volume Scheme for a Corrosion Model

Abstract

In this paper, we study the numerical approximation of a system of partial dif-ferential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In particular, we are interested in the convergence of a numerical scheme consisting in an implicit Euler scheme in time and a Scharfetter-Gummel finite volume scheme in space

Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation

“…In our case, we notice that the only term which differ from [6,10] is the term |A u,1 − A u,1 |. For this reason, we only prove that |A u,1 (m) − A u,1 (m)| → 0 as m ↑ ∞ in the sequel.…”

“…3.1 in [12]). For a rigorous proof of this fact one can read Lemmas 2.1 and 2.2 in [10]. Eventually, for each m, we define (s m , u m , v m ) a sequence of solution to (S) with s m = s ∆tm and w m = w hm,∆tm .…”

“…In order to prove that (s, u, v) satisfies (S3), (S4) and (S5), we follow some ideas developed in [6,10]. For sake of simplicity, for a given mesh T and a given time step ∆t, we define:…”

“…For this reason, we only prove that |A u,1 (m) − A u,1 (m)| → 0 as m ↑ ∞ in the sequel. For the other terms we refer to [6,10]. By definition of A u,1 (m), we have…”

Study of a pseudo-stationary state for a corrosion model: Existence and numerical approximation

“…In [9], ChainaisHillairet and Lacroix-Violet proves the existence of a solution in a simplified case where only electrons and cations are taken into account and therefore the domain is fixed. Convergence of backward Euler scheme in time and finite volume scheme in space for the same simplified system has been established in [7]. Chainais-Hillairet and Lacroix-Violet have also proved in [8] the existence of a steady state for the two species system on a fixed domain, while the convergence of a finite volume scheme is studied in [6].…”