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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Author: Alexandre L. Madureira
Journal: Math. Comp. 78 (2009), 25-34
MSC (2000): Primary 35J05, 35J25, 65N12, 65N15, 65N30
Published electronically: June 26, 2008
MathSciNet review: 2448695
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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: http://dx.doi.org/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
Published electronically: 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.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.