Exponential homogenization of linear second order elliptic PDEs with periodic coefficients

V Kamotski, K Matthies, V P Smyshlyaev

Research output: Contribution to journalArticle

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Abstract

A problem of homogenization of a divergence‐type second order uniformly elliptic operator is considered with arbitrary bounded rapidly oscillating periodic coefficients, either with periodic “outer” boundary conditions or in the whole space. It is proved that if the right‐hand side is Gevrey regular (in particular, analytic), then by optimally truncating the full two‐scale asymptotic expansion for the solution one obtains an approximation with an exponentially small error. The optimality of the exponential error bound is established for a one‐dimensional example by proving the analogous lower bound.
LanguageEnglish
Pages1565-1587
Number of pages23
JournalSIAM Journal on Mathematical Analysis (SIMA)
Volume38
Issue number5
DOIs
StatusPublished - 12 Jan 2007

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Exponential Bound
Oscillating Coefficients
Elliptic PDE
Periodic Coefficients
Linear Order
Elliptic Operator
Homogenization
Error Bounds
Asymptotic Expansion
Divergence
Optimality
Lower bound
Boundary conditions
Arbitrary
Approximation

Cite this

Exponential homogenization of linear second order elliptic PDEs with periodic coefficients. / Kamotski, V; Matthies, K; Smyshlyaev, V P.

In: SIAM Journal on Mathematical Analysis (SIMA), Vol. 38, No. 5, 12.01.2007, p. 1565-1587.

Research output: Contribution to journalArticle

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