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.
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Received September 11, 1998 / Published online April 20, 2000
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Matache, A., Babuška, I. & Schwab, C. Generalized p-FEM in homogenization. Numer. Math. 86, 319–375 (2000). https://doi.org/10.1007/PL00005409
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DOI: https://doi.org/10.1007/PL00005409