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Semi-discrete finite difference multiscale scheme for a concrete corrosion model: a priori estimates and convergence

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Abstract

We study a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction–diffusion equations coupled with an ordinary differential equation. We prove energy and regularity estimates and use them to get the necessary compactness of the approximate solutions. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the solution to our system.

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Vladimír Chalupecký

  2. Faculty of Mathematics and Computer Science, Center for Analysis, Scientific Computing and Applications (CASA), Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Adrian Muntean

Authors
  1. Vladimír Chalupecký
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  2. Adrian Muntean
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Correspondence to Vladimír Chalupecký.

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Chalupecký, V., Muntean, A. Semi-discrete finite difference multiscale scheme for a concrete corrosion model: a priori estimates and convergence. Japan J. Indust. Appl. Math. 29, 289–316 (2012). https://doi.org/10.1007/s13160-012-0060-6

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  • DOI: https://doi.org/10.1007/s13160-012-0060-6

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