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

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  • Šolín, Pavel
  • Červený, Jakub
  • Doležel, Ivo

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.

Suggested Citation

  • Šolín, Pavel & Červený, Jakub & Doležel, Ivo, 2008. "Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 117-132.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:1:p:117-132
    DOI: 10.1016/j.matcom.2007.02.011
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    References listed on IDEAS

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    1. Šolín, Pavel & Vejchodský, Tomáš & Zítka, Martin & Ávila, Francisco, 2007. "Imposing orthogonality to hierarchic higher-order finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 211-217.
    2. Vejchodský, Tomáš & Šolín, Pavel & Zítka, Martin, 2007. "Modular hp-FEM system HERMES and its application to Maxwell’s equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 223-228.
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    Cited by:

    1. Nikolayev, Denys & Kubík, Zdeněk & Karban, Pavel & Skála, Jiří, 2016. "Impedance analysis of transmission line cells for EMC applications using Agros2D," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 381-387.
    2. Koudela, Lukáš & Kotlan, Václav, 2015. "High-speed rotation induction heating in thermal clamping technology," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 445-455.
    3. Devloo, Philippe R.B. & Farias, Agnaldo M. & Gomes, Sônia M. & de Siqueira, Denise, 2016. "Two-dimensional hp adaptive finite element spaces for mixed formulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 126(C), pages 104-122.

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