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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.
Original language  English 

Pages (fromto)  15651587 
Number of pages  23 
Journal  SIAM Journal on Mathematical Analysis (SIMA) 
Volume  38 
Issue number  5 
DOIs  
Publication status  Published  12 Jan 2007 
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Dive into the research topics of 'Exponential homogenization of linear second order elliptic PDEs with periodic coefficients'. Together they form a unique fingerprint.Projects
 1 Finished

ESTABLISHMENT OF THE UNIVERSITY OF BATH CENTRE FOR COMPLEX S YSTEMS  O/HEAD SPLIT SM75% EN25%
Budd, C. (PI), Almond, D. (CoI), Britton, N. (CoI), Hunt, G. (CoI), Hurn, M. (CoI) & Smyshlyaev, V. P. (CoI)
Engineering and Physical Sciences Research Council
29/11/04 → 28/11/09
Project: Research council