@article{AIHPB_2004__40_2_153_0, author = {Bourgeat, Alain and Piatnitski, Andrey}, title = {Approximations of effective coefficients in stochastic homogenization}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {153--165}, publisher = {Elsevier}, volume = {40}, number = {2}, year = {2004}, doi = {10.1016/j.anihpb.2003.07.003}, mrnumber = {2044813}, zbl = {1058.35023}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.003/} }
TY - JOUR AU - Bourgeat, Alain AU - Piatnitski, Andrey TI - Approximations of effective coefficients in stochastic homogenization JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2004 SP - 153 EP - 165 VL - 40 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.003/ DO - 10.1016/j.anihpb.2003.07.003 LA - en ID - AIHPB_2004__40_2_153_0 ER -
%0 Journal Article %A Bourgeat, Alain %A Piatnitski, Andrey %T Approximations of effective coefficients in stochastic homogenization %J Annales de l'I.H.P. Probabilités et statistiques %D 2004 %P 153-165 %V 40 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.003/ %R 10.1016/j.anihpb.2003.07.003 %G en %F AIHPB_2004__40_2_153_0
Bourgeat, Alain; Piatnitski, Andrey. Approximations of effective coefficients in stochastic homogenization. Annales de l'I.H.P. Probabilités et statistiques, Volume 40 (2004) no. 2, pp. 153-165. doi : 10.1016/j.anihpb.2003.07.003. http://www.numdam.org/articles/10.1016/j.anihpb.2003.07.003/
[1] Modeling and Computation in Environmental Sciences, in: Notes in Numerical Fluids Mechanics, vol. 59, 1997, pp. 13-24. | MR | Zbl
, ,[2] Dynamics of Fluids in Porous Media, Elsevier, New York, 1972.
,[3] Nonlinear stochastic homogenization and ergodic theory, J. Reine Angew. Math. 368 (1986) 28-42. | MR | Zbl
, ,[4] Asymptotic Analysis of Periodic Structures, North Holland, Amsterdam, 1978. | MR | Zbl
, , ,[5] Eléments de comparaison entre la méthode d'homogénéisation et la méthode de prise de moyenne avec fermeture, C. R. Acad. Sci. Paris Sér. II 306 (1988) 463-466. | MR | Zbl
, , ,[6] Stochastic two-scale convergence in the mean and applications, J. Reine Angew. Math. 456 (1994) 19-51. | MR | Zbl
, , ,[7] Effective equations of two-phase flow in random media, Cal. Var. PDE 8 (1998) 1-31.
, , ,[8] Linear Operators, Part I, General Theory, Interscience, 1963. | MR | Zbl
, ,[9] Representation of grid block permeability in coarse scale models of randomly heterogeneous porous media, Water Resources Res. 28 (1992) 1791-1800.
,[10] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. | MR | Zbl
, ,[11] Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids 11 (1963) 357-372. | Zbl
,[12] Homogenization and Porous Media, IAM, vol. 6, Springer-Verlag, Berlin, 1997. | MR | Zbl
(Ed.),[13] Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, New York, 1994. | MR | Zbl
, , ,[14] The averaging of random operators, Math. USSR Sb. 109 (1979) 188-202. | MR | Zbl
,[15] Geometric aspects of homogenization, Russian Math. Surv. 44 (1989) 91-144. | MR | Zbl
,[16] Controlled Diffusion Processes, Application of Mathematics, vol. 14, Springer-Verlag, New York, 1980. | MR | Zbl
,[17] Plates, Laminates and Shells. Asymptotic Analysis and Homogenization, Series on Advances in Mathematics for Applied Sciences, vol. 52, World Scientific, River Edge, NJ, 2000. | MR | Zbl
, ,[18] Stochastic Homogenization and Ergodic Theory, in: , , (Eds.), Proceedings ERICE 1984, Lecture Notes in Mathematics, vol. 1190, Springer-Verlag, 1986, Chapter 15. | MR | Zbl
,[19] Approximation of effective conductivity of ergodic media by periodization, Probab. Theory Related Fields 125 (2003) 225-258. | MR | Zbl
,[20] Boundary value problems with rapidly oscillating random coefficients. Random fields. Rigorous results in statistical mechanics and quantum field theory, Esztergom 1979, Colloq. Math. Soc. Janos Bolyai 27 (1981) 835-873. | MR | Zbl
, ,[21] On the homogenization and the simulation of random materials, Eur. J. Mech., A/Solids 11 (5) (1992) 585-607. | MR | Zbl
,[22] On the error of averaging of symmetric elliptic systems, Math. USSR-Izv. 35 (1) (1990) 183-201. | MR | Zbl
, ,[23] Calculating equivalent permeability: A review, Adv. Water Resour. 20 (1997) 253-278.
, ,[24] Averaging of symmetric diffusion in random medium, Sibirskii Mat. Zh. 27 (4) (1986) 167-180. | EuDML | MR | Zbl
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