Approximations of effective coefficients in stochastic homogenization

 Access to full text

 Full (PDF)

1. [1] A. Badea, A. Bourgeat, Modeling and Computation in Environmental Sciences, in: Notes in Numerical Fluids Mechanics, vol. 59, 1997, pp. 13-24. Zbl0895.76064MR1487420
2. [2] J. Bear, Dynamics of Fluids in Porous Media, Elsevier, New York, 1972. Zbl1191.76001
3. [3] G. Dal Maso, L. Modica, Nonlinear stochastic homogenization and ergodic theory, J. Reine Angew. Math.368 (1986) 28-42. Zbl0582.60034MR850613
4. [4] A. Bensoussan, J.-L. Lions, G. Papanicolaou, Asymptotic Analysis of Periodic Structures, North Holland, Amsterdam, 1978. Zbl0404.35001MR503330
5. [5] A. Bourgeat, M. Quintard, S. Whitaker, Eléments de comparaison entre la méthode d'homogénéisation et la méthode de prise de moyenne avec fermeture, C. R. Acad. Sci. Paris Sér. II306 (1988) 463-466. Zbl0637.45008MR979154
6. [6] A. Bourgeat, A. Mikelic, S. Wright, Stochastic two-scale convergence in the mean and applications, J. Reine Angew. Math.456 (1994) 19-51. Zbl0808.60056MR1301450
7. [7] A. Bourgeat, S.M. Kozlov, A. Mikelić, Effective equations of two-phase flow in random media, Cal. Var. PDE8 (1998) 1-31. Zbl0824.35099
8. [8] N. Dunford, J.T. Schwartz, Linear Operators, Part I, General Theory, Interscience, 1963. Zbl0084.10402MR1009162
9. [9] L.J. Durlofski, Representation of grid block permeability in coarse scale models of randomly heterogeneous porous media, Water Resources Res.28 (1992) 1791-1800. 
10. [10] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977. Zbl0361.35003MR473443
11. [11] R. Hill, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids11 (1963) 357-372. Zbl0114.15804
12. [12] Hornung U. (Ed.), Homogenization and Porous Media, IAM, vol. 6, Springer-Verlag, Berlin, 1997. Zbl0872.35002MR1434315
13. [13] V.V. Jikov, S.M. Kozlov, O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, New York, 1994. Zbl0838.35001MR1329546
14. [14] S.M. Kozlov, The averaging of random operators, Math. USSR Sb.109 (1979) 188-202. Zbl0415.60059MR542557
15. [15] S.M. Kozlov, Geometric aspects of homogenization, Russian Math. Surv.44 (1989) 91-144. Zbl0706.49029MR998362
16. [16] N. Krylov, Controlled Diffusion Processes, Application of Mathematics, vol. 14, Springer-Verlag, New York, 1980. Zbl0459.93002MR601776
17. [17] T. Lewinski, J. Telega, Plates, Laminates and Shells. Asymptotic Analysis and Homogenization, Series on Advances in Mathematics for Applied Sciences, vol. 52, World Scientific, River Edge, NJ, 2000. Zbl0965.74003MR1758600
18. [18] L. Modica, Stochastic Homogenization and Ergodic Theory, in: Conti, De Giorgi, Gianessi (Eds.), Proceedings ERICE 1984, Lecture Notes in Mathematics, vol. 1190, Springer-Verlag, 1986, Chapter 15. Zbl0597.49010MR858358
19. [19] H. Owhadi, Approximation of effective conductivity of ergodic media by periodization, Probab. Theory Related Fields125 (2003) 225-258. Zbl1040.60025MR1961343
20. [20] G. Papanicolaou, S.R.S. Varadhan, 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 Bolyai27 (1981) 835-873. Zbl0499.60059MR712714
21. [21] K. Sab, On the homogenization and the simulation of random materials, Eur. J. Mech., A/Solids11 (5) (1992) 585-607. Zbl0766.73008MR1184222
22. [22] A.V. Pozhidaev, V.V. Yurinskii, On the error of averaging of symmetric elliptic systems, Math. USSR-Izv.35 (1) (1990) 183-201. Zbl0702.35254MR1018751
23. [23] Ph. Renard, G. DeMarsily, Calculating equivalent permeability: A review, Adv. Water Resour.20 (1997) 253-278. 
24. [24] V.V. Yurinski, Averaging of symmetric diffusion in random medium, Sibirskii Mat. Zh.27 (4) (1986) 167-180. Zbl0614.60051MR867870

1. Frédéric Legoll, Florian Thomines, On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients
2. Pierre-Louis Lions, Panagiotis E. Souganidis, Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications
3. Antoine Gloria, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations
4. Jean-Christophe Mourrat, Variance decay for functionals of the environment viewed by the particle
5. Daniel Boivin, Tail estimates for homogenization theorems in random media
6. Antoine Gloria, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations