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

Claire Chainais-Hillairet (1) , Benoît Merlet (1) , Antoine Zurek (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems

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

Domaines: Mathématiques [math]

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⟩