Geodesic
Averagind of difference schemes
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 351-369 
S. M. Kozlov. Averagind of difference schemes. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 351-369. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a1/
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     author = {S. M. Kozlov},
     title = {Averagind of difference schemes},
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     volume = {57},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_57_2_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author considers a natural class of difference equations whose coefficients have micro-inhomogeneities. A general compactness theorem is established, asserting that the solutions of these difference equations can converge only to solutions of differential equations as the lattice is refined. Difference equations with random micro-inhomogeneous coefficients are studied separately; their averaging properties are determined. Bibliography: 12 titles.

[1] Kunin L. A., Teoriya uprugikh sred s mikrostrukturoi, Nauka, M., 1975

[2] Seshu S., Rid M., Lineinye grafy i elektricheskie tsepi, Nauka, M., 1971

[3] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[4] Anshelevich V. V., Khanin K. M., Sinai Ya. G., “Symmetric random walks in random environments”, Commun. Math. Phys., 86:1 (1982), 1–22 | DOI | MR

[5] Kozlov S. M., “Metod usredneniya i bluzhdaniya v neodnorodnykh sredakh”, UMN, 40:2 (1985), 61–120 | MR

[6] Zhikov V. V., Kozlov S. M., Oleinik O. A., Kha T'en Ngoan, “Usrednenie i $G$-skhodimost differentsialnykh operatorov”, UMN, 34:5 (1979), 65–133 | MR | Zbl

[7] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[8] Spagnolo S., “Sulla convergenza di solutioni di equazioni paraboliche ed ellittice”, Ann. Scoula Norm. Sup. Risa, 22 (1968), 577–597 | MR

[9] Zhikov V. V., Kozlov S. M., Oleinik O. A., “O $G$-skhodimosti parabolicheskikh operatorov”, UMN, 36:1 (1981), 11–58 | MR

[10] Marchellini P., “Convergence of second order liniar elliptic operators”, Boll. Un. Mat. Ital., 5:16 (1979), 278–290 | MR

[11] Bovin V. P.. Vaskin V. V., Shneiberg I. Ya., “Rekursivnye modeli v teorii protekaniya”, TMF, 54:2 (1983), 268–279 | MR

[12] Kirpatrik S., “Perkolyatsiya i provodimost”, Sb. NFTT, no. 7, Mir, M., 248–292