Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM

In this paper we present a new automatic adaptivity algorithm for the hp-FEM which is based on arbitrary-level hanging nodes and local element projections. The method is very simple to implement compared to other existing hp-adaptive strategies, while its performance is comparable or superior. This...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2008-02, Vol.77 (1), p.117-132
Main Authors: Šolín, Pavel, Červený, Jakub, Doležel, Ivo
Format: Article
Language:English
Subjects:
35B50
65N60
Automatic hp-adaptivity
Constrained approximation
Hanging nodes
hp-FEM
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Summary:In this paper we present a new automatic adaptivity algorithm for the hp-FEM which is based on arbitrary-level hanging nodes and local element projections. The method is very simple to implement compared to other existing hp-adaptive strategies, while its performance is comparable or superior. This is demonstrated on several numerical examples which include the L-shape domain problem, a problem with internal layer, and the Girkmann problem of linear elasticity. With appropriate simplifications, the proposed technique can be applied to standard lower-order and spectral finite element methods.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2007.02.011