Composite finite elements for the approximation of PDEs on domains with complicated micro-structures |
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Authors: | W Hackbusch SA Sauter |
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Institution: | Institut für Informatik und Praktische Mathematik, Universit?t Kiel, D-24098 Kiel, Germany; email: sas@numerik.uni-kiel.de, Fax: 0431 8804054, DE
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Abstract: | Summary. Usually, the minimal dimension of a finite element space is closely related to the geometry of the physical object of interest.
This means that sometimes the resolution of small micro-structures in the domain requires an inadequately fine finite element
grid from the viewpoint of the desired accuracy. This fact limits also the application of multi-grid methods to practical
situations because the condition that the coarsest grid should resolve the physical object often leads to a huge number of
unknowns on the coarsest level. We present here a strategy for coarsening finite element spaces independently of the shape
of the object. This technique can be used to resolve complicated domains with only few degrees of freedom and to apply multi-grid
methods efficiently to PDEs on domains with complex boundary. In this paper we will prove the approximation property of these
generalized FE spaces.
Received June 9, 1995 / Revised version received February 5, 1996 |
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Keywords: | Mathematics Subject Classification (1991): 65D05 65N12 65N15 65N30 65N50 65N55 |
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