Homogenization Problem in a Domain with Double Oscillating Boundary

Abstract EN

In this paper, we study the convergence of solutions for homogenization problems about the Poisson equation in a domain with double oscillating locally periodic boundary.

Such a problem arises in the processing of devices with very small features.

We utilize second-order Taylor expansion of boundary data in combination with boundary correctors to obtain the convergence rate in H1-norm.

This work explores the domain with double oscillating boundary and also shows the influence of the amplitudes and periods of the oscillations to convergence rates of solutions.