Homogenization of a Nonlinear Elliptic Boundary Value Problem Modeling Galvanic Currents

@article{Bhat2006HomogenizationOA,
  title={Homogenization of a Nonlinear Elliptic Boundary Value Problem Modeling Galvanic Currents},
  author={Yermal Sujeet Bhat and Shari Moskow},
  journal={Multiscale Modeling & Simulation},
  year={2006},
  volume={5},
  pages={149-169}
}
We study a nonlinear elliptic boundary value problem arising from electrochemistry in the study of heterogeneous electrode surfaces. The boundary condition is of exponential type (Butler–Volmer) and has a periodic structure. We find a limiting or effective problem as the period approaches zero, along with a first order correction. We establish convergence estimates and provide numerical experiments.