Geodesic
Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 457-480

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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.

DOI : 10.1051/m2an/2018002
Classification : 65M08, 65M12
Keywords: Finite volume scheme, carbonation model, convergence analysis, free-boundary system

Chainais-Hillairet, Claire 1 ; Merlet, Benoît 1 ; Zurek, Antoine 1

1 
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     title = {Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {457--480},
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Chainais-Hillairet, Claire; Merlet, Benoît; Zurek, Antoine. Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 457-480. doi: 10.1051/m2an/2018002

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