| Issue |
ESAIM: M2AN
Volume 52, Number 2, March–April 2018
|
|
|---|---|---|
| Page(s) | 457 - 480 | |
| DOI | https://doi.org/10.1051/m2an/2018002 | |
| Published online | 04 June 2018 | |
Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation
Univ. Lille, CNRS, UMR 8524, Inria – Laboratoire Paul Painlevé,
59000
Lille, France
* Corresponding author: antoine.zurek@math.univ-lille1.fr
Received:
16
March
2017
Accepted:
12
January
2018
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.
Mathematics Subject Classification: 65M08 / 65M12
Key words: Finite volume scheme / carbonation model / convergence analysis / free-boundary system
© The authors. Published by EDP Sciences, SMAI 2018
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