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Volume 25, Issue 6
Linearization of a Nonlinear Periodic Boundary Condition Related to Corrosion Modeling

Y. S. Bhat & S. Moskow

J. Comp. Math., 25 (2007), pp. 645-660.

Published online: 2007-12

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  • Abstract

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two- and three-dimensional case and provide two-dimensional numerical experiments.

  • Keywords

Galvanic corrosion, Homogenization, Nonlinear elliptic boundary value problem, Butler-Volmer boundary condition, Robin boundary condition.

  • AMS Subject Headings

35J65, 35Q72.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-645, author = {Y. S. Bhat and S. Moskow}, title = {Linearization of a Nonlinear Periodic Boundary Condition Related to Corrosion Modeling}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {6}, pages = {645--660}, abstract = {

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two- and three-dimensional case and provide two-dimensional numerical experiments.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8720.html} }
TY - JOUR T1 - Linearization of a Nonlinear Periodic Boundary Condition Related to Corrosion Modeling AU - Y. S. Bhat & S. Moskow JO - Journal of Computational Mathematics VL - 6 SP - 645 EP - 660 PY - 2007 DA - 2007/12 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8720.html KW - Galvanic corrosion, Homogenization, Nonlinear elliptic boundary value problem, Butler-Volmer boundary condition, Robin boundary condition. AB -

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two- and three-dimensional case and provide two-dimensional numerical experiments.

Y. S. Bhat and S. Moskow. (2007). Linearization of a Nonlinear Periodic Boundary Condition Related to Corrosion Modeling. Journal of Computational Mathematics. 25 (6). 645-660. doi:
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