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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 21
Edited by: M. Papadrakakis and B.H.V. Topping
Paper II.3

A Multiscale Finite-Element-Method

E. Rank and R. Krause

Numerische Methoden und Informationsverarbeitung, Universität Dortmund, Dortmund-Eichlinghofen, Germany

Full Bibliographic Reference for this paper
E. Rank, R. Krause, "A Multiscale Finite-Element-Method", in M. Papadrakakis, B.H.V. Topping, (Editors), "Advances in Post and Preprocessing for Finite Element Technology", Civil-Comp Press, Edinburgh, UK, pp 69-75, 1994. doi:10.4203/ccp.21.2.3
The paper describes a hierarchical overlay of a p-version finite element approximation on a coarse mesh and an h-approximation on a geometrically independent fine mesh. The length scales of the local problem may be some orders of magnitude below the scale of the global problem. Despite the incompatibility of the meshes used, continuity can easily be guaranteed in the proposed method. The paper shows, how finite element meshes can be constructed adaptively on the local and the global meshes. It is demonstrated how a block-iteration allows a simple and efficient implementation of the method. Typical fields of application and the efficiency of the method are shown in a numerical example.

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