### Abstract

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 |

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### Cite this

*SIAM Journal on Mathematical Analysis (SIMA)*,

*38*(5), 1565-1587. https://doi.org/10.1137/060651045

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

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis (SIMA)*, vol. 38, no. 5, pp. 1565-1587. https://doi.org/10.1137/060651045

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TY - JOUR

T1 - Exponential homogenization of linear second order elliptic PDEs with periodic coefficients

AU - Kamotski, V

AU - Matthies, K

AU - Smyshlyaev, V P

PY - 2007/1/12

Y1 - 2007/1/12

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1137/060651045

U2 - 10.1137/060651045

DO - 10.1137/060651045

M3 - Article

VL - 38

SP - 1565

EP - 1587

JO - SIAM Journal on Mathematical Analysis (SIMA)

JF - SIAM Journal on Mathematical Analysis (SIMA)

SN - 0036-1410

IS - 5

ER -