A multiscale finite element method for partial differential equations posed in domains with rough boundaries

Madureira, Alexandre

doi:10.1090/S0025-5718-08-02159-5

A multiscale finite element method for partial differential equations posed in domains with rough boundaries
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by Alexandre L. Madureira;

Math. Comp. 78 (2009), 25-34

DOI: https://doi.org/10.1090/S0025-5718-08-02159-5

Published electronically: June 26, 2008

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Abstract:

We propose and analyze a finite element scheme of multiscale type to deal with elliptic partial differential equations posed in domains with rough boundaries. There is no need to assume that the boundary is periodic in any sense, so the method is quite general. On the other hand, if the boundary is periodic we prove convergence of the scheme.

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