TY - JOUR
T1 - Linearization of a Nonlinear Periodic Boundary Condition Related to Corrosion Modeling
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 - <p style="text-align: justify;">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.</p>