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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 |
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Pages (from-to) | 1565-1587 |

Number of pages | 23 |

Journal | SIAM Journal on Mathematical Analysis (SIMA) |

Volume | 38 |

Issue number | 5 |

DOIs | |

Publication status | Published - 12 Jan 2007 |

## Fingerprint 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., Almond, D., Britton, N., Hunt, G., Hurn, M. & Smyshlyaev, V. P.

Engineering and Physical Sciences Research Council

29/11/04 → 28/11/09

Project: Research council

## Cite this

Kamotski, V., Matthies, K., & Smyshlyaev, V. P. (2007). Exponential homogenization of linear second order elliptic PDEs with periodic coefficients.

*SIAM Journal on Mathematical Analysis (SIMA)*,*38*(5), 1565-1587. https://doi.org/10.1137/060651045