Numerical methods for elliptic partial differential equations with rapidy oscillating coefficients

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 1-2, 2003, Pages 47-76

  Conca, C ^a   Natesan, S ^b  

^a DEPARTAMENTO DE FÍSICA   (Chile)

^b Center for Mathematical Modeling   (Chile)

Author keywords

Bloch waves; Correctors; Homogenization; Numerical solution of differential equations; Periodic structures

Indexed keywords

DIFFERENTIAL EQUATIONS; NUMERICAL METHODS; OSCILLATORS (MECHANICAL); COMPUTATIONAL METHODS; COMPUTER APPLICATIONS; HOMOGENIZATION METHOD; PERIODIC STRUCTURES;

ELLIPTIC OPERATORS;

COMPUTER APPLICATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATION;

APPROXIMATION FUNCTION; AUXILIARY FUNCTIONS; BLOCH WAVES; CORRECTORS; ELLIPTIC PARTIAL DIFFERENTIAL EQUATION; HOMOGENIZATION PROBLEMS; NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS; TAYLOR APPROXIMATION;

EID: 0037414944     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(02)00500-5     Document Type: Article

References (20)

1. Avellaneda M. Berlyand L. Clouet J.-F. Frequency-dependent acoustics of composites with interfaces, SIAM J. Appl. Math. 60 (2000) 2143-2181.
2. M. Avellaneda, T. Hou, G. Papanicolaou, Finite difference approximations for partial differential equations with rapidly oscillating coefficients, Math. Modell. Numer. Anal. 25 (1991) 693-710.
3. J. Bear, Use of models in decision making, in: T. Dracos, F. Stauffer (Eds.), Transport and Reactive Process in Aquifers, Balkema, Rotterdam, 1994, pp. 3-9.
4. A. Bensoussan, J.-L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
5. F. Bloch, CUber die quantenmechanik der electronen in kristallgittern, Z. Phys. 52 (1928) 555-600.
6. J. Bourgat, Numerical experiments of the homogenization method for operators with periodic coe.cients, Technical Report 277, Institut de Recherche dInformatique et dAutomatique, Le Chesnay, France, 1978.
7. J. Bourgat, H. Lanchon, Application of the homogenization method to composite materials with periodic structures, Technical Report 208, Institut de Recherche dInformatique et dAutomatique, Le Chesnay, France, 1976.
8. Y. Capdeboscq, Homogenization of a di.usion equation with drift, C.R. Acad. Sci. Paris Serie I 327(1998) 807-812.
9. C. Conca, S. Natesan, M. Vanninathan, Numerical experiments with the Bloch-Floquet approach in homogenization, Working Paper, 2002.
10. C. Conca, R. Orive, M. Vanninathan, Bloch approximation in homogenization and applications, SIAM J. Math. Anal. 33 (2002) 1166-1198.
11. C. Conca, J. Planchard, M. Vanninathan, Fluids and Periodic Structures, No. 38 in Research in Applied Mathematics, John Wiley/Masson, New York/Paris, 1995.
12. C. Conca, M. Vanninathan, Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math. 57(1997) 1639-1659.
13. T. Hou, X. Wu, A multiscale .nite element method for elliptic problems in composite materials and porous media, J. Comput. Phys. 134 (1997) 169-189.
14. S. Kesavan, Homogenization of elliptic eigenvalue problems: Part 2, Appl. Math. Optim. 5 (1979) 197-216.
15. J.-L. Lions, Some Methods in the Mathematical Analysis of Systems and Their Control, Gordon and Breach, Beijing, New York, 1981.
16. A. Matache, I. Babu ska, C. Schwab, Generalized p-fem in homogenization, Numer. Math. 86 (2000) 319-375.
17. R. Morgan, I. Babu ska, An approach for constructing families of homogenized equations for periodic media I: Integral representation and its consequences, SIAM J. Math. Anal. 22 (1991) 1-15.
18. J. Planchard, Methodes Mathematiques en Neutronique, Collection de la Direction des Etudes et Recherches dEDF, Eyrolles, Paris, 1995.
19. E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, vol. 127, Springer-Verlag, Berlin, 1980.
20. M. Vanninathan, Homogenization and eigenvalue problems in perforated domains, Proc. Indian Acad. Sci. Math. Sci. 90 (1981) 239-271.