Free Access
Issue
ESAIM: M2AN
Volume 46, Number 1, January-February 2012
Page(s) 1 - 38
DOI https://doi.org/10.1051/m2an/2011018
Published online 22 July 2011
  1. S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of N-body Schrödinger operators, Mathematical Notes 29. Princeton University Press, Princeton, NJ (1982). [Google Scholar]
  2. R. Alicandro, M. Cicalese and A. Gloria, Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity. Arch. Ration. Mech. Anal. 200 (2011) 881–943. [CrossRef] [Google Scholar]
  3. A. Bourgeat and A. Piatnitski, Approximations of effective coefficients in stochastic homogenization. Ann. Inst. H. Poincaré 40 (2004) 153–165. [Google Scholar]
  4. P. Caputo and D. Ioffe, Finite volume approximation of the effective diffusion matrix: the case of independent bond disorder. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003) 505–525. [CrossRef] [MathSciNet] [Google Scholar]
  5. T. Delmotte, Inégalité de Harnack elliptique sur les graphes. Colloq. Math. 72 (1997) 19–37. [MathSciNet] [Google Scholar]
  6. A. Dykhne, Conductivity of a two-dimensional two-phase system. Sov. Phys. JETP 32 (1971) 63–65. Russian version: Zh. Eksp. Teor. Fiz. 59 (1970) 110–5. [Google Scholar]
  7. W. E, P.B. Ming and P.W. Zhang, Analysis of the heterogeneous multiscale method for elliptic homogenization problems. J. Amer. Math. Soc. 18 (2005) 121–156. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Gloria, Reduction of the resonance error – Part 1: Approximation of homogenized coefficients. Math. Models Methods Appl. Sci., to appear. [Google Scholar]
  9. A. Gloria and F. Otto, An optimal variance estimate in stochastic homogenization of discrete elliptic equations. Ann. Probab. 39 (2011) 779–856. [CrossRef] [Google Scholar]
  10. A. Gloria and F. Otto, An optimal error estimate in stochastic homogenization of discrete elliptic equations. Ann. Appl. Probab., to appear. [Google Scholar]
  11. A. Gloria and F. Otto, Quantitative estimates in stochastic homogenization of linear elliptic equations. In preparation. [Google Scholar]
  12. T.Y. Hou and X.H. Wu, A Multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169–189. [CrossRef] [MathSciNet] [Google Scholar]
  13. V.V. Jikov, S.M. Kozlov and O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin (1994). [Google Scholar]
  14. T. Kanit, S. Forest, I. Galliet, V. Mounoury and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Sol. Struct. 40 (2003) 3647–3679. [CrossRef] [Google Scholar]
  15. S.M. Kozlov, The averaging of random operators. Mat. Sb. (N.S.) 109 (1979) 188–202, 327. [MathSciNet] [Google Scholar]
  16. S.M. Kozlov, Averaging of difference schemes. Mat. Sb. 57 (1987) 351–369. [CrossRef] [Google Scholar]
  17. R. Künnemann, The diffusion limit for reversible jump processes on Formula with ergodic random bond conductivities. Commun. Math. Phys. 90 (1983) 27–68. [CrossRef] [Google Scholar]
  18. J.A. Meijerink and H.A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp. 31 (1977) 148–162. [MathSciNet] [Google Scholar]
  19. A. Naddaf and T. Spencer, Estimates on the variance of some homogenization problems. Preprint (1998). [Google Scholar]
  20. H. Owhadi, Approximation of the effective conductivity of ergodic media by periodization. Probab. Theory Relat. Fields 125 (2003) 225–258. [CrossRef] [MathSciNet] [Google Scholar]
  21. G.C. Papanicolaou and S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, in Random fields I, II (Esztergom, 1979), Colloq. Math. Soc. János Bolyai 27. North-Holland, Amsterdam (1981) 835–873. [Google Scholar]
  22. X. Yue and W. E, The local microscale problem in the multiscale modeling of strongly heterogeneous media: effects of boundary conditions and cell size. J. Comput. Phys. 222 (2007) 556–572. [CrossRef] [MathSciNet] [Google Scholar]
  23. V.V. Yurinskii, Averaging of symmetric diffusion in random medium. Sibirskii Matematicheskii Zhurnal 27 (1986) 167–180. [MathSciNet] [Google Scholar]

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