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

Authors:
Pavel Šolín;Jakub ervený;Ivo Doleel
Affiliations:
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968-0514, USA and Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, Pra ...;Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968-0514, USA and Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, Pra ...;Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, Prague, CZ 10800
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

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.