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Interior error estimate for periodic homogenization (1109.1908v1)
Published 9 Sep 2011 in math.NA
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 $\Omega\subset Rn$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates.