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Published in:
2018 | OriginalPaper | Chapter
Convergence Rates, Part I
Author : Zhongwei Shen
Published in: Periodic Homogenization of Elliptic Systems
Publisher: Springer International Publishing
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Let $$\mathcal{L}_\varepsilon\,\,=\,\,\mathrm{-div}(\mathit{A}(\mathit{x}/\varepsilon) \nabla )$$ for ε > 0, where $$\mathit{A}(\mathit{y})\,\,=\,\,(\mathit{a}_\mathit{i,j}^{\alpha\beta} \, (\mathit{y})) $$ is 1-periodic and satisfies a certain ellipticity condition. Let $$\mathcal{L}_0\,\,=\,\,\mathrm{-div}(\mathit{\hat{A}}\nabla), $$ , where $$\mathit{\hat{A}}\,\,=\,\,(\hat{\mathit{a}}_{\mathit{ij}}^{\alpha\beta}) $$ denotes the matrix of effective coefficients, given by (2.2.16).