Abstract:

The paper is concerned with the convergence rates of solutions for homogenization of m$-order elliptic equations with the mixed Dirichlet-Neumann boundary conditions. Our approach, which involves smoothing operator and thus avoids the estimates of the boundary discrepancies terms. As a consequence, we establish the rates of convergence in $H_{0}^{m}$ as well as $L^{2}$. This work may be regarded as an extension of the usage smoothing operator to the case of higher-order equations with mixed boundary condition settings.

Key words: Homogenization, Higher-order equations, Convergence rates, Mixed boundary condition