Free access
Issue
ESAIM: M2AN
Volume 36, Number 4, July/August 2002
Page(s) 537 - 572
DOI http://dx.doi.org/10.1051/m2an:2002025
Published online 15 September 2002
  1. I. Babuska and A.K. Aziz, Survey lectures on the mathematical foundation of the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz Ed., Academic Press, New York (1973) 5-359.
  2. A. Bensoussan, J.L. Lions and G. Papanicolau, Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam (1978).
  3. D. Cioranescu and J. Saint Jean Paulin, Homogenization of Reticulated Structures. Springer-Verlag, New York (1999).
  4. T.Y. Hou and X.H. Wu, A Multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169-189. [CrossRef] [MathSciNet]
  5. T.Y. Hou, X.H. Wu and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comp. 68 (1999) 913-943. [CrossRef] [MathSciNet]
  6. A.-M. Matache, Spectral- and p-Finite Elements for problems with microstructure, Ph.D. thesis, ETH Zürich (2000).
  7. A.-M. Matache, I. Babuska and C. Schwab, Generalized p-FEM in Homogenization. Numer. Math. 86 (2000) 319-375. [CrossRef] [MathSciNet]
  8. A.-M. Matache and M.J. Melenk, Two-scale regularity for homogenization problems with non-smooth fine-scale geometries, submitted.
  9. A.-M. Matache and C. Schwab, Finite dimensional approximations for elliptic problems with rapidly oscillating coefficients, in Multiscale Problems in Science and Technology, N. Antonic, C.J. van Duijn, W. Jäger and A. Mikelic Eds., Springer-Verlag (2002) 203-242.
  10. R.C. Morgan and I. Babuska, An approach for constructing families of homogenized solutions for periodic media, I: An integral representation and its consequences, II: Properties of the kernel. SIAM J. Math. Anal. 22 (1991) 1-33. [CrossRef] [MathSciNet]
  11. C. Schwab, p- and hp- Finite Element Methods. Oxford Science Publications (1998).
  12. C. Schwab and A.-M. Matache, High order generalized FEM for lattice materials, in Proc. of the 3rd European Conference on Numerical Mathematics and Advanced Applications, Finland, 1999, P. Neittaanmäki, T. Tiihonen and P. Tarvainen Eds., World Scientific, Singapore (2000).
  13. B. Szab ó and I. Babuska, Finite Element Analysis. John Wiley & Sons, Inc. (1991).
  14. O.A. Oleinik, A.S. Shamaev and G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization. North-Holland (1992).

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