Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition. (arXiv:1002.3793v1 [math.NA])

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition. (arXiv:1002.3793v1 [math.NA]): "

We study a two-scale reaction-diffusion system with nonlinear reaction terms
and a nonlinear transmission condition (remotely ressembling Henry's law) posed
at air-liquid interfaces. We prove the rate of convergence of the two-scale
Galerkin method proposed in Muntean & Neuss-Radu (2009) for approximating this
system in the case when both the microstructure and macroscopic domain are
two-dimensional. The main difficulty is created by the presence of a boundary
nonlinear term entering the transmission condition. Besides using the
particular two-scale structure of the system, the ingredients of the proof
include two-scale interpolation-error estimates, an interpolation-trace
inequality, and improved regularity estimates.

"