Sparsity Optimized High Order Finite Element Functions on Simplices

  • Sven BeuchlerEmail author
  • Veronika Pillwein
  • Joachim Schöberl
  • Sabine Zaglmayr
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)


This article reports several results on sparsity optimized basis functions for hp-FEM on triangular and tetrahedral finite element meshes obtained within the Special Research Program “Numerical and Symbolic Scientific Computing” and within the Doctoral Program “Computational Mathematics” both supported by the Austrian Science Fund FWF under the grants SFB F013 and DK W1214, respectively. We give an overview on the sparsity pattern for mass and stiffness matrix in the spaces L 2, H 1, H({ div}) and H(curl). The construction relies on a tensor-product based construction with properly weighted Jacobi polynomials.


Sparse Optimization Jacobi Polynomials Duffy Transformation Edge Bubble Function Bubble Interior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by the FWF-projects P20121-N12 and P20162-N18, the Austrian Academy of Sciences, the Spezialforschungsbereich “Numerical and Symbolic Scientific Computing” (SFB F013) , the doctoral program “Computational Mathematics” (W1214) and the FWF Start Project Y-192 on “3D hp-Finite Elements: Fast Solvers and Adaptivity”.


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Copyright information

© Springer-Verlag/Wien 2012

Authors and Affiliations

  • Sven Beuchler
    • 1
    Email author
  • Veronika Pillwein
    • 2
  • Joachim Schöberl
    • 3
  • Sabine Zaglmayr
    • 4
  1. 1.Institute for Numerical SimulationUniversity of BonnBonnGermany
  2. 2.Research Institute for Symbolic ComputationJohannes Kepler University LinzLinzAustria
  3. 3.Institute for Analysis and Scientific ComputingTU WienWienAustria
  4. 4.Computer Simulation TechnologyDarmstadtGermany

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