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Imposing orthogonality to hierarchic higher-order finite elements

Author

Listed:
  • Šolín, Pavel
  • Vejchodský, Tomáš
  • Zítka, Martin
  • Ávila, Francisco

Abstract

We propose a new class of hierarchic higher-order finite elements suitable for the hp-FEM discretization of symmetric linear elliptic problems. These elements use shape functions which are partially orthonormal on the reference domain under the energetic inner product induced by the elliptic problem. We present numerical experiments showing excellent conditioning properties of the new partially orthogonal shape functions compared to other popular sets of hierarchic shape functions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:76:y:2007:i:1:p:211-217
    DOI: 10.1016/j.matcom.2007.01.025
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    Cited by:

    1. 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.

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