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In this paper, we construct approximations of the microscopic solution of anonlinear reaction--diffusion equation in a domain consisting of twobulk-domains, which are separated by a thin layer with a periodic heterogeneousstructure. The size of the heterogeneities and thickness of the layer are oforder $\epsilon$, where the parameter $\epsilon$ is small compared to thelength scale of the whole domain. In the limit $\epsilon \to 0$, when the thinlayer reduces to an interface $\Sigma$ separating two bulk domains, amacroscopic model with effective interface conditions across $\Sigma$ isobtained. Our approximations are obtained by adding corrector terms to themacroscopic solution, which take into account the oscillations in the thinlayer and the coupling conditions between the layer and the bulk domains. Tovalidate these approximations, we prove error estimates with respect to$\epsilon$. Our approximations are constructed in two steps leading to errorestimates of order $\epsilon^{\frac12}$ and $\epsilon$ in the $H^1$-norm.

Correctors and error estimates for reaction-diffusion processes through  thin heterogeneous layers in case of homogenized equations with interface  diffusion