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.
Mots-clés : Finite volume scheme, carbonation model, convergence analysis, free-boundary system
@article{M2AN_2018__52_2_457_0,
author = {Chainais-Hillairet, Claire and Merlet, Beno{\^\i}t and Zurek, Antoine},
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},
publisher = {EDP-Sciences},
volume = {52},
number = {2},
year = {2018},
doi = {10.1051/m2an/2018002},
zbl = {1404.65109},
mrnumber = {3834432},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2018002/}
}
TY - JOUR AU - Chainais-Hillairet, Claire AU - Merlet, Benoît AU - Zurek, Antoine TI - Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 457 EP - 480 VL - 52 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2018002/ DO - 10.1051/m2an/2018002 LA - en ID - M2AN_2018__52_2_457_0 ER -
%0 Journal Article %A Chainais-Hillairet, Claire %A Merlet, Benoît %A Zurek, Antoine %T Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 457-480 %V 52 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2018002/ %R 10.1051/m2an/2018002 %G en %F M2AN_2018__52_2_457_0
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. http://www.numdam.org/articles/10.1051/m2an/2018002/
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