Homogenization via p-FEM for problems with microstructure

Applied Numerical Mathematics

Volumn 33, Issue 1, 2000, Pages 43-59

  Matache, A M ^a   Schwab, Ch ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; MICROSTRUCTURE; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; THEOREM PROVING;

HIERARCHICAL MODELING; HOMOGENIZATION;

FINITE ELEMENT METHOD;

EID: 0034190245     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00069-0     Document Type: Article

References (10)

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2. I. Babuška, B.Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. Part 1: Boundary value problems for linear elliptic equation of second order, SIAM J. Math. Anal. 19 (1988) 172-203.
3. A. Bensoussan, J.L. Lions, G. Papanicolau, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
4. T. Hou, X.-H. Wu, Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients, Math. Comp., to appear.
5. A.M. Matache, Spectral and p-Finite Elements for Homogenization Problems, Doctoral Dissertation, in preparation.
6. A.M. Matache, I. Babuška, C. Schwab, Generalized p-FEM in homogenization, Report 99-01, Seminar for Applied Mathematics, ETH Zürich, Switzerland.
7. J.M. Melenk, On n-widths for elliptic problems, Report 98-02, Seminar for Applied Mathematics, ETH Zürich, Switzerland; J. Math. Anal. Appl., to appear.
8. R.C. Morgan, I. Babuška, An approach for constructing families of homogenized equations for periodic media. I: An integral representation and its consequences, SIAM J. Math. Anal. 22 (1) (1991) 1-15; II: Properties of the kernel, SIAM J. Math. Anal. 22 (1) (1991) 16-33.
9. R.C. Morgan, I. Babuška, An approach for constructing families of homogenized equations for periodic media. I: An integral representation and its consequences, SIAM J. Math. Anal. 22 (1) (1991) 1-15; II: Properties of the kernel, SIAM J. Math. Anal. 22 (1) (1991) 16-33.
10. O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North- Holland, Amsterdam, 1992.