Bloch approximation in homogenization on bounded domains

Conca, C. ; Orive, R. ; Vanninathan, M. (2005) Bloch approximation in homogenization on bounded domains Asymptotic Analysis, 41 (1). pp. 71-91. ISSN 0921-7134

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The classical problem of homogenization deals with elliptic operators in periodically oscillating media of small period ε > 0 and the asymptotic behavior of solution uε of boundary value problems associated with such operators. In a previous work [Conca et al., SIAM J. Math. Anal. 33 (2002), 1166-1198], the authors introduced what is called Bloch approximation which provided energy norm approximation for the solution in RN. This paper continues with the above development and proposes a modified Bloch approximation. This function takes into account boundary effects. Its connection with the first order classical correctors is also established with the corresponding error estimate. All the proofs are worked out entirely in the Fourier-Bloch space.

Item Type:Article
Source:Copyright of this article belongs to IOS Press.
Keywords:Homogenization; Bloch Waves; Correctors
ID Code:55368
Deposited On:18 Aug 2011 07:07
Last Modified:18 May 2016 07:40

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