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

Author(s): Alexandre L. Madureira.
Journal: Math. Comp.
MSC (2000): Primary 35J05, 35J25, 65N12, 65N15, 65N30
Posted: 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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Additional Information:

Alexandre L. Madureira
Affiliation: Coordenação de Matemática Aplicada e Computacional, Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, CEP 25651-070 Petrópolis - RJ, Brazil
Email: alm@lncc.br

DOI: 10.1090/S0025-5718-08-02159-5
PII: S 0025-5718(08)02159-5
Received by editor(s): February 12, 2007
Received by editor(s) in revised form: October 5, 2007
Posted: June 26, 2008
Additional Notes: The author was partially supported by the CNPq/Brazil Projects 306104/2004-0 and 486026/2006-0, and also by FAPERJ Project APQ1 E-26/170.629/2006.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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