Open Access
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
  1. T. Aiki and A. Muntean. Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structure. Adv. Math. Sci. Appl. 19 (2009) 109–129. [Google Scholar]
  2. T. Aiki and A. Muntean, Large time behavior of solutions to a moving-interface problem modeling concrete carbonation. Commun. Pure Appl. Anal. 9 (2010) 1117–1129. [CrossRef] [Google Scholar]
  3. T. Aiki and A. Muntean, A free-boundary problem for concrete carbonation: front nucleation and rigorous justification of the Formula -law of propagation. Interfaces Free Bound. 15 (2012) 167–180. [CrossRef] [Google Scholar]
  4. T. Aiki and A. Muntean, Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data. Nonlinear Anal. 93 (2013) 3–14. [CrossRef] [Google Scholar]
  5. C. Bataillon, F. Bouchon, C. Chainais-Hillairet, J. Fuhrmann, E. Hoarau and R. Touzani, Numerical methods for the simulation of a corrosion model with a moving oxide layer. J. Comput. Phys. 231 (2012) 6213–6231. [CrossRef] [Google Scholar]
  6. M. Bessemoulin-Chatard, A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Schafetter-Gummel scheme. Numer. Math. 121 (2012) 637–670. [CrossRef] [Google Scholar]
  7. K. Brenner, C. Cancès and D. Hilhorst, Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure. Comput. Geosci. 17 (2013) 573–597. [CrossRef] [Google Scholar]
  8. C. Chainais-Hillairet and C. Bataillon, Mathematical and numerical study of a corrosion model. Numer. Math. 110 (2008) 689–716. [CrossRef] [Google Scholar]
  9. C. Chainais-Hillairet and J. Droniou, Finite volume schemes for non-coercive elliptic problems with Neumann boundary conditions. IMA J. Numer. Anal. 31 (2011) 61–85. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Chainais-Hillairet, P.-L. Colin and I. Lacroix-Violet, Convergence of a finite volume scheme for a corrosion model. Int. J. Finite 12 (2015) 1–27. [Google Scholar]
  11. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods. Vol. VII of Handbook of Numerical Analysis. North-Holland (2000) 713–1020. [Google Scholar]
  12. T. Gallouët and J.-C. Latché, Compactness of discrete approximate solutions to parabolic PDEs – application to a turbulence model. Commun. Pure Appl. Anal. 11 (2012) 2371–2391. [CrossRef] [Google Scholar]
  13. A.M. Il’in. A difference scheme for a differential equation with a small parameter multiplying the highest derivative. Mat. Zametki 6 (1969) 237–248. [Google Scholar]
  14. R.D. Lazarov, I.D. Mishev and P.S. Vassilevski, Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33 (1996) 31–55. [CrossRef] [MathSciNet] [Google Scholar]
  15. S.A. Meyer, M. Peter, A. Muntean and M. Böhm, Dynamics of the internal reaction layer arising during carbonation of concrete. Chem. Eng. Sci. 62 (2007) 1125–1137. [CrossRef] [Google Scholar]
  16. A. Muntean, Error bounds on semi-discrete finite element approximations of a moving-boundary system arising in concrete corrosion. Int. J. Numer. Anal. Model. 5 (2008) 353–372. [Google Scholar]
  17. A. Muntean and M. Böhm, On a moving reaction layer model for the prediction of the service life of concrete structures, in Proc. of the International Conference on Performance Based Engineering for 21st Century University of Iasi, Romania, edited by G. Yagawa, M. Kikuchi, G.M. Atanasiu and C. Bratianu (2004) 72–77. [Google Scholar]
  18. A. Muntean and M. Böhm, On a prediction model for the service life of concrete structures based on moving interfaces, in Proc. of the Second International Conference on Lifetime-Oriented Design Concepts Ruhr University Bochum, Germany, edited by F. Stangenberg, O.T. Bruhns, D. Hartmann and G. Meschke (2004) 209–218. [Google Scholar]
  19. A. Muntean and M. Böhm, A moving-boundary problem for concrete carbonation: global existence and uniqueness of solutions. J. Math. Anal. Appl. 350 (2009) 234–251. [CrossRef] [Google Scholar]
  20. A. Muntean and M. Neuss-Radu, A multiscale Galerkin approach for a class of nonlinear coupled reaction-diffusion systems in complex media. J. Math. Anal. Appl. 371 (2010) 705–718. [CrossRef] [Google Scholar]
  21. F.A. Radu, A. Muntean, I.S. Pop, N. Suciu and O. Kolditz, A mixed finite element discretization scheme for a concrete carbonation model with concentration-dependent porosity. J. Comput. Appl. Math. 246 (2013) 74–85. [CrossRef] [Google Scholar]
  22. D.L. Scharfetter and H.K. Gummel, Large signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Devices 16 (1969) 64–77. [CrossRef] [Google Scholar]
  23. Q. Zhang, Mathematical modeling and numerical study of carbonation in porous concrete materials. Appl. Math. Comput. 281 (2016) 16–27. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you