Interior error estimate for periodic homogenization

Abstract

In a previous article about the homogenization of the classical problem of diff usion in a bounded domain with su ciently smooth boundary we proved that the error is of order ${\epsilon }^{1/2}$. Now, for an open set with su ciently smooth boundary $C^{1,1}$ and homogeneous Dirichlet or Neuman limits conditions we show that in any open set strongly included in the error is of order $\epsilon$. If the open set $\Omega \subset R^n$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates.

References in corpus (1)

• Error estimate and unfolding for periodic homogenization

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