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About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows
Homogenization: In mathematics or physics?
1. | Department of Mathematics, Soochow University, Suzhou 215006, China |
2. | High Speed Aerodynamics Institute, China Aerodynamisc Development and Research Center, Mianyang 622661, China |
References:
[1] |
G. Allaire, Homogenization et convergence a deux echelles,, application a un probleme de convection diffusion. C.R.Acad. Sci. Paris, 312 (1991), 581.
|
[2] |
G. Allaire, Homogenization and two-scale convergence,, SIAM J. Math. Anal., 23 (1992), 1482.
doi: 10.1137/0523084. |
[3] |
I. Babuška, Solution of problem with interfaces and singularities,, in Mathematical aspects of finite elements in partial differential equations, (1974), 213. Google Scholar |
[4] |
I. Babuška, Homogenization approach in engineering,, Lecture notes in economics and mathematical systems, 134 (1976), 137.
|
[5] |
I. Babuška, Homogenization and its application. Mathematical and computational problems,, Numerical solution of partial differential equations, III (1976), 89.
|
[6] |
I. Babuška, The computational aspects of the homogenization problem,, Computing methods in applied sciences and engineering, 704 (1976), 309.
|
[7] |
A. Bensousan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures,, North-Holland, (1978).
|
[8] |
D. Cioranescu and P. Donato, An Introduction to Homogenization,, Oxford Lecture Series in Mathematics and Its Applications, 17 (1999).
|
[9] |
S. M. Kozlov, The averaging of random operators,, Mat.Sb.(N.S), 109 (1979), 188.
|
[10] |
K. Lichtenecker, Die dielektrizitätskonstante natürlicher und künstlicher mischkörper,, Phys. Zeitschr., XXVII (1926), 115. Google Scholar |
[11] |
J. C. Maxwell, A Treatise on Electricity and Magnetism,, 3rd Ed., (1881). Google Scholar |
[12] |
F. Murat and L. Tartar, H-convergence,, Topics in the Mathematical Modelling of Composite Materials, 31 (1997), 21.
doi: 10.1007/978-1-4612-2032-9_3. |
[13] |
G. Nguestseng, A general convergence result for a functional related to the theory of homogenization,, SIAM J. Math. Anal., 20 (1989), 608.
doi: 10.1137/0520043. |
[14] |
O. A. Olenik and A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization,, Studies in mathematics and its applications, 26 (1992).
|
[15] |
S. Poisson, Second mémoire sur la théorie du magnétisme,, Mem. Acad. France 5, 5 (1822). Google Scholar |
[16] |
S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all' equatione del calore,, Ann. Scuola Norm. Sup. Pisa, 21 (1967), 657.
|
[17] |
T. A. Suslina, Homogenization of a stationary periodic maxwell system,, St. Petersburg Math. J., 16 (2005), 863.
doi: 10.1090/S1061-0022-05-00883-6. |
[18] |
L. Tartar, Compensated compactness and partial differential equations,, in Nolinear Analysis and Mechanics: Heriot-Watt Symposium, 39 (1979), 136.
|
[19] |
L. Tartar, H-measure, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations,, Proc. Roy. Soc. Edinburgh, 115 (1990), 193.
doi: 10.1017/S0308210500020606. |
[20] |
T. Yu and X. Yue, Residual-free bubble methods for numerical homogenization of elliptic problems,, Commun. Math. Sci., 9 (2011), 1163.
doi: 10.4310/CMS.2011.v9.n4.a12. |
[21] |
V. V. Zhikov, Some estimates from homogenization theory,, (Russian) Dokl. Akad. Nauk, 406 (2006), 597.
|
[22] |
V. V. Zhikov and O. A. Oleinik, Homogenization and G-convergence of differential operators,, Russ. Math. Surv., 34 (1979), 65. Google Scholar |
[23] |
V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals,, Springer Berlin, (1994).
doi: 10.1007/978-3-642-84659-5. |
show all references
References:
[1] |
G. Allaire, Homogenization et convergence a deux echelles,, application a un probleme de convection diffusion. C.R.Acad. Sci. Paris, 312 (1991), 581.
|
[2] |
G. Allaire, Homogenization and two-scale convergence,, SIAM J. Math. Anal., 23 (1992), 1482.
doi: 10.1137/0523084. |
[3] |
I. Babuška, Solution of problem with interfaces and singularities,, in Mathematical aspects of finite elements in partial differential equations, (1974), 213. Google Scholar |
[4] |
I. Babuška, Homogenization approach in engineering,, Lecture notes in economics and mathematical systems, 134 (1976), 137.
|
[5] |
I. Babuška, Homogenization and its application. Mathematical and computational problems,, Numerical solution of partial differential equations, III (1976), 89.
|
[6] |
I. Babuška, The computational aspects of the homogenization problem,, Computing methods in applied sciences and engineering, 704 (1976), 309.
|
[7] |
A. Bensousan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures,, North-Holland, (1978).
|
[8] |
D. Cioranescu and P. Donato, An Introduction to Homogenization,, Oxford Lecture Series in Mathematics and Its Applications, 17 (1999).
|
[9] |
S. M. Kozlov, The averaging of random operators,, Mat.Sb.(N.S), 109 (1979), 188.
|
[10] |
K. Lichtenecker, Die dielektrizitätskonstante natürlicher und künstlicher mischkörper,, Phys. Zeitschr., XXVII (1926), 115. Google Scholar |
[11] |
J. C. Maxwell, A Treatise on Electricity and Magnetism,, 3rd Ed., (1881). Google Scholar |
[12] |
F. Murat and L. Tartar, H-convergence,, Topics in the Mathematical Modelling of Composite Materials, 31 (1997), 21.
doi: 10.1007/978-1-4612-2032-9_3. |
[13] |
G. Nguestseng, A general convergence result for a functional related to the theory of homogenization,, SIAM J. Math. Anal., 20 (1989), 608.
doi: 10.1137/0520043. |
[14] |
O. A. Olenik and A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization,, Studies in mathematics and its applications, 26 (1992).
|
[15] |
S. Poisson, Second mémoire sur la théorie du magnétisme,, Mem. Acad. France 5, 5 (1822). Google Scholar |
[16] |
S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all' equatione del calore,, Ann. Scuola Norm. Sup. Pisa, 21 (1967), 657.
|
[17] |
T. A. Suslina, Homogenization of a stationary periodic maxwell system,, St. Petersburg Math. J., 16 (2005), 863.
doi: 10.1090/S1061-0022-05-00883-6. |
[18] |
L. Tartar, Compensated compactness and partial differential equations,, in Nolinear Analysis and Mechanics: Heriot-Watt Symposium, 39 (1979), 136.
|
[19] |
L. Tartar, H-measure, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations,, Proc. Roy. Soc. Edinburgh, 115 (1990), 193.
doi: 10.1017/S0308210500020606. |
[20] |
T. Yu and X. Yue, Residual-free bubble methods for numerical homogenization of elliptic problems,, Commun. Math. Sci., 9 (2011), 1163.
doi: 10.4310/CMS.2011.v9.n4.a12. |
[21] |
V. V. Zhikov, Some estimates from homogenization theory,, (Russian) Dokl. Akad. Nauk, 406 (2006), 597.
|
[22] |
V. V. Zhikov and O. A. Oleinik, Homogenization and G-convergence of differential operators,, Russ. Math. Surv., 34 (1979), 65. Google Scholar |
[23] |
V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals,, Springer Berlin, (1994).
doi: 10.1007/978-3-642-84659-5. |
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