Abstract
The implementation of a generalized Finite Element Method (FEM) for problems with coefficients or geometry that oscillate locally at a small length scale ε≪1 is described. Two-scale FE-spaces are combined conformingly with standard FE. Numerical experiments show that the complexity of the algorithm is independent of the micro length scale ε.
Similar content being viewed by others
REFERENCES
Cioranescu, D., and Donato, P. (1999). An Introduction to Homogenization, Oxford University Press.
Duarte, C. A., Babuška, I., and Oden, J. T. (2000). Generalized finite element methods for three-dimensional structural mechanics problems. Computers and Structures, 215–232.
Hou, T. Y., and Wu, X. H. (1997). A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134, 169–189.
Matache, A.-M., Babuška, I., and Schwab, Ch. (2000). Generalized p-FEM in homogenization. Numer. Math. 86, 319–375.
Matache, A.-M. (2000). Spectral and p-Finite Elements for Problems with Micrstructure, Dissertation, ETH Zürich.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rüegg, A.W. Implementation of Generalized Finite Element Methods for Homogenization Problems. Journal of Scientific Computing 17, 671–681 (2002). https://doi.org/10.1023/A:1015139117673
Issue Date:
DOI: https://doi.org/10.1023/A:1015139117673