Abstract
In this paper, we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form \( \frac{\partial } {{\partial _{x_i } }}(a^{ij} (\frac{x} {\varepsilon })\frac{{\partial u^\varepsilon (x)}} {{\partial _{x_j } }}) = f(x) \). Assuming n = 2 and u 0 ∈ W 1,∞(Ω), we present an error estimate between the homogenization solution u 0(x) and the exact solution u ɛ(x) on the Sobolev space L∞(Ω).
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He, W., Cui, J. Error estimate of the homogenization solution for elliptic problems with small periodic coefficients on L ∞(Ω). Sci. China Math. 53, 1231–1252 (2010). https://doi.org/10.1007/s11425-010-0078-7
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DOI: https://doi.org/10.1007/s11425-010-0078-7
Keywords
- multi-scale homogenization theory
- homogenization solution
- second order elliptic equations with small periodic coefficients