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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2018

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

Abstract

In this paper we define and study a finite volume scheme for a concrete carbonation model proposed by Aiki and Muntean in [Adv. Math. Sci. Appl. 19 (2009) 109–129]. The model consists in a system of two weakly coupled parabolic equations in a varying domain whose length is governed by an ordinary differential equation. The numerical sheme is obtained by a Euler discretisation in time and a Scharfetter-Gummel discretisation in space. We establish the convergence of the scheme. As a by-product, we obtain existence of a solution to the model. Finally, some numerical experiments show the efficiency of the scheme.
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Dates and versions

hal-02922751 , version 1 (27-02-2017)
hal-02922751 , version 2 (05-12-2018)
hal-02922751 , version 3 (26-08-2020)

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Claire Chainais-Hillairet, Benoît Merlet, Antoine Zurek. Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (2), pp.457-480. ⟨10.1051/m2an/2018002⟩. ⟨hal-02922751v3⟩
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