95-6   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Wolfgang Hackbusch, Stefan A. Sauter:

A New Finite Element Approach for Problems Containing Small Geometric Details

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 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.

Bibliographical note: Archivum mathematicum 34: 105-117, 1998.

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