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| Título | Rate of convergence for correctors in almost periodic homogenization |
| Publication Type | Unpublished |
| Year of Publication | 2005 |
| Authors | Bondarenko A, Bouchitté G, Mascarenhas L, Mahadevan R |
| Series Title | Preprint |
| Abstract | In the homogenization of second order elliptic equations with periodic coefficients, it is well known that the rate of convergence of the corrector un - u^{hom} in the L^2 norm is 1/n, the same as the scale of periodicity (see Jikov et al [7]). It is possible to have the same rate of convergence in the case of almost periodic coefficients under some stringent structural conditions on the coefficients (see Kozlov [8]). The goal of this note is to construct almost periodic media where the rate of convergence is lower than 1/n. To that aim, in the one dimensional setting, we introduce a family of random almost periodic coefficients for which we compute, using Fourier series analysis, the mean rate of convergence r_n (mean with respect to the random parameter). This allows us to present examples where we find r_n » 1/n^r for every r > 0, showing a big contrast with the random case considered by Bourgeat and Piatnitski [3] where r_n » 1/√n. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2005/2_05.pdf |