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A new finite element approach for problems containing small geometric details


Hackbusch, W; Sauter, S (1998). A new finite element approach for problems containing small geometric details. Archivum Mathematicum, 34(1):105-117.

Abstract

In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called {\it Composite Finite Elements }are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization of PDEs without requiring periodicity of the data.

Abstract

In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called {\it Composite Finite Elements }are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization of PDEs without requiring periodicity of the data.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Finite Elements, Shortley-Weller discretization, complicated boundary
Language:English
Date:1998
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:26
Publisher:Masaryk University, Brno, CR
ISSN:0044-8753
Additional Information:Proceedings of the 9th Conference on Differential Equations and their Applications held in Brno, August 25–29, 1997
Free access at:Related URL. An embargo period may apply.
Related URLs:http://www.emis.de/journals/AM/98-1/index.html (Publisher)

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