Multiscale finite element for problems with highly oscillatory coefficients

Numerische Mathematik

Volumn 90, Issue 3, 2002, Pages 459-486

  Efendiev, Yalchin R ^a   Wu, Xiao Hui ^b,c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c EXXONMOBIL UPSTREAM RESEARCH COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036002578     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100274     Document Type: Article

References (19)

1. S. Agmon: Lectures on elliptic boundary value problems. Princeton, N.J.: Van Nostrand 1965
2. G. Allaire, M. Briane: Multiscale convergence and reiterated homogenization. Proc. Roy. Soc. Edinburgh A Math. 126, 297-342 (1996)
3. M. Avellaneda, F-H. Lin: Compactness methods in the theory of homogenization. Commun Pure Appl. Math. XL, 803-843 (1989)
4. A. Azzam: Smoothness properties of bounded solution of dirichlet problem for elliptic equations in regions with corners on the boundaries. Canad. Math. Bull. 23 (1980)
5. I. Babuška, G. Caloz, E. Osborn: Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 31, 945-981 (1994)
6. A. Bensoussan, J. L. Lions, G. Papanicolaou: Asymptotic Analysis for Periodic Structure, volume 5 of Studies in Mathematics and Its Applications. Amsterdam: North-Holland 1978
7. F. Brezzi, L. Franca, T. Hughes, A. Russo: b is equal to integral of g. Comput. Methods Appl. Mech. Engrg. 145, 329-339 (1997)
8. P. G. Ciarlet: The finite element method for elliptic problems. Amsterdam: North-Holland 1978
9. Y. R. Efendiev, T. Y. Hou, X. H. Wu: The convergence of non-conforming multiscale finite element methods. SIAM in Num. Anal. 37, (3) 888-910 (1998)
10. Y.R. Efendiev: The multiscale finite element method and its applications. Ph.D thesis, California Institute of Technology, 1999
11. T. Y. Hou, X. H. Wu: A multiscale finite element method for elliptic problems in composite materials and porous media. J. Computat. Phy. 134, 169-189 (1997)
12. T. Y. Hou, X. H. Wu: A multiscale finite element method for PDEs with oscillatory coefficients. Notes on Numerical Fluid Mechanics 70, 58-69 (1999)
13. T. Y. Hou, X. H. Wu, Z. Cai: Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comp. 68 (227), 913-943 (1999)
14. T. Hughes, G. Feijoo, L. Mazzei, J. Quincy: The variational multiscale method - a paradigm for computational mechanics. Comput. Methods Appl. Mech. Engrg. 166, 3-24 (1998)
15. V. V. Jikov, S. M. Kozlov, O. A. Oleinik: Homogenization of differential operators and integral functionals. Berlin Heidelberg New York: Springer 1994
16. O. A. Ladyzhenskaia, N. N. Uraltseva: Linear and quasilinear elliptic eqautions. New York: Academic Press 1968
17. E. Oriordan, M. Stynes: A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in 2 dimensions. Math. Comp. 57, 47-62 (1991)
18. R. Scott: Interpolated boundary conditions in the finite element method. SIAM J. Numer. Anal. 12, 404-427 (1975)
19. L. Ying: Infinite Element Methods. Beijing: Peking University Press 1995