Abstract:

In this paper, we study the convergence rates of solutions for homogenization of the oscillating Robin mixed boundary value problems. The main difficulty of this work is due to the oscillating factor on the Robin boundary as well as boundary discrepancies. Thanks to the duality approach, we could handle the oscillatory integral. As a consequence, we establish the rates of convergence in $H^{1}$ and $L^{2}$, which depends on the dimension explicitly. This work may be regarded as an extension of the duality approach as well as smoothing operators for oscillating Robin mixed boundary value problems.

Key words: Homogenization, Convergence rates, Duality approach, Smoothing operators, Oscillatory integral