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Generalized p-FEM in Homogenization

by A. M. Matache and I. Babuska and Ch. Schwab

(Report number 1999-01)

Abstract
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.

Keywords:

@Techreport{MBS99_236,
  author = {A. M. Matache and I. Babuska and Ch. Schwab},
  title = {Generalized p-FEM in Homogenization},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1999-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1999/1999-01.pdf },
  year = {1999}
}

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