Interior error estimate for periodic homogenization
Provides refined error bounds for numerical homogenization, relevant to analysts working on multiscale PDEs.
This paper improves the error estimate for periodic homogenization in bounded domains from ε^{1/2} to ε in interior subdomains, assuming C^{1,1} boundary and Dirichlet or Neumann conditions. For polygonal/polyhedral domains, global and interior error estimates are also provided.
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 $ε^{1/2}$. 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 $ε$. If the open set $Ω\subset R^n$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates.