EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 46 / No 1 (January-February 2012) ESAIM: M2AN, 46 1 (2012) 1-38 References
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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you