Summary. A new finite element method for elliptic problems with locally periodic microstructure of length \(\varepsilon >0\) is developed and analyzed. It is shown that the method converges, as \(\varepsilon \rightarrow 0\), to the solution of the homogenized problem with optimal order in \(\varepsilon\) and exponentially in the number of degrees of freedom independent of \(\varepsilon > 0\). The computational work of the method is bounded independently of \(\varepsilon\). Numerical experiments demonstrate the feasibility and confirm the theoretical results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received September 11, 1998 / Published online April 20, 2000
Rights and permissions
About this article
Cite this article
Matache, A., Babuška, I. & Schwab, C. Generalized p-FEM in homogenization. Numer. Math. 86, 319–375 (2000). https://doi.org/10.1007/PL00005409
Issue Date:
DOI: https://doi.org/10.1007/PL00005409