Finite difference approximations for partial differential equations with rapidly oscillating coefficients
ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 6, pp. 693-710.
@article{M2AN_1991__25_6_693_0,
     author = {Avellaneda, M. and Hou, Th. Y. and Papanicolaou, G. C.},
     title = {Finite difference approximations for partial differential equations with rapidly oscillating coefficients},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {693--710},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {25},
     number = {6},
     year = {1991},
     mrnumber = {1135990},
     zbl = {0755.65088},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1991__25_6_693_0/}
}
TY  - JOUR
AU  - Avellaneda, M.
AU  - Hou, Th. Y.
AU  - Papanicolaou, G. C.
TI  - Finite difference approximations for partial differential equations with rapidly oscillating coefficients
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1991
SP  - 693
EP  - 710
VL  - 25
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1991__25_6_693_0/
LA  - en
ID  - M2AN_1991__25_6_693_0
ER  - 
%0 Journal Article
%A Avellaneda, M.
%A Hou, Th. Y.
%A Papanicolaou, G. C.
%T Finite difference approximations for partial differential equations with rapidly oscillating coefficients
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1991
%P 693-710
%V 25
%N 6
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1991__25_6_693_0/
%G en
%F M2AN_1991__25_6_693_0
Avellaneda, M.; Hou, Th. Y.; Papanicolaou, G. C. Finite difference approximations for partial differential equations with rapidly oscillating coefficients. ESAIM: Modélisation mathématique et analyse numérique, Tome 25 (1991) no. 6, pp. 693-710. http://archive.numdam.org/item/M2AN_1991__25_6_693_0/

[1] E. Degiorgi and S. Spagnolo, Sulla convergenza degli integrali dell'energia per operatori ellitici del secundo ordine, Boll. I.M.I., 8, 391-411, 1973. | MR | Zbl

[2] I. Babuska, Solution of interface problems by homogenization I, II, III, SIAM J. Math. Analysis, 7, 603-345, 635-645, and 8, 923-937, 1976. | MR | Zbl

[3] L. Tartar, Cours Peccot, Paris 1977.

[4] A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978. | MR | Zbl

[5] E. Sanchez-Palencia, Nonhomogeneous Media and Vibration Theory, Springer, 1980. | MR | Zbl

[6] G. Papanicolaou and S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, at Proceedings of Conference on Random Fields, Esztergom, Hungary, 1979, published in Séria Colloquia Mathematica Societatis Janos Bolyai, 27, 835-873, North Holland, 1981. | MR | Zbl

[7] V. V. Zhikov, S. M. Kozlov, O. Oleinik and Kha T'En Ngoan, AVERAGING and G-convergence of differential operators, Uspekhi Mat. Nauk. 34, 65-133, 1979. | MR | Zbl

[8] N. Bahvalov and G. Panachenko, Average of processes in periodic media, Nauka, Moscow, 1984. | Zbl

[9] S. Kozlov, The method of averaging and walks in inhomogeneous environments, Uspekhi Mat. Nauk 40, 61-120, 1985. | MR | Zbl

[10] G. Papanicolaou, Macroscopic properties of composites, bubbly fluids, suspensions and related problems, in Les méthodes de Fhomogénéization : Théorie et applications en physique, CEA-EDF-INRIA séries 57, 229-318, Eyrolles, Paris, 1985. | MR

[11] J. L. Lions, Remarques sur les problèmes d'homogénéization dans les milieux à structure périodique et sur quelques problèmes raides, in Les méthodes de l'homogénéization : Théorie et applications en physique, CEA-EDF-INRIA séries 57, 129-228, Eyrolles, Paris, 1985. | MR

[12] F. Murat and L. Tartar, Calcul des variations et homogénéization, in Les méthodes de l'homogénéization : Théorie et applications en physique, CEA-EDF-INRIA séries 57, 319-370, Eyrolles, Paris, 1985. | MR

[13] B. Engquist, Computation of oscillatory solutions to hyperbolic differential equations, to appear. Also in Lecture Notes in Math. 1270, 10-22, Springer, 1987. | MR | Zbl

[14] B. Engquist and T. Hou, Particle method approximation of oscillatory solutions to hyperbolic differential equations, SIAM J. Numer. Anal. 26, 289-319, 1989. | MR | Zbl

[15] B. Engquist and T. Hou, Computation of oscillatory solutions to hyperbolic differential equations using particle methods, Lecture Notes in Math., 1360, 68-82, 1988. | MR | Zbl

[16] L. Tartar, Solutions oscillantes des équations de Carleman, Séminaire Goulaouic-Meyer-Schwartz, 1981. | Numdam | MR | Zbl

[17] D. Mclaughlin, G. Papanicolaou andL. Tartar, Weak limits of semilinear hyperbolic equations with oscillating data, Springer Lecture Notes in Phys., 230, 277-289, 1985. | Zbl

[18] R. Kuhnemann, The diffusion limit for reversible jump processes on Zd with ergodic random bond conductivities, Comm. Math. Phys., 90, 27-68, 1983. | MR | Zbl

[19] R. Figari, E. Orlandi and G. Papanicolaou, Diffusive behavior of a random walk in a random medium, in « Stochastic Analysis » by K. Ito, 105-120, North Holland, 1984. | MR | Zbl

[20] V. Arnold and A. Avez, Ergodic Problems of Classical Mechanics, Benjamin, New York, 1968. | MR | Zbl

[21] K. Golden and G. Papanicolaou, Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., 90, 473-491, 1983. | MR