Automatic hp-Adaptivity With Arbitrary-Level Hanging Nodes

In this paper we present a new algorithm for fully automatic hp-adaptivity for elliptic problems based on arbitrary-level hanging nodes and local element projections. The algorithm is very simple to implement compared to best existing hp-adaptive strategies while its performance is comparable and sometimes superior. Numerical examples include the L-shape domain problem and a problem with internal layer (standard test cases with known exact solutions) as well as the challenging Girkmann problem of linear elasticity. With appropriate simplifications, the proposed technique can be applied to standard lower-order and spectral finite element methods. AMS subject classification: 35B50, 65N60

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