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Sparse shape functions for tetrahedral p-FEM using integrated Jacobi polynomials

Summary

In this paper, we investigate the discretization of an elliptic boundary value problem in 3D by means of the hp-version of the finite element method using a mesh of tetrahedrons. We present several bases based on integrated Jacobi polynomials in which the element stiffness matrix has \({\mathcal{O}}(p^3)\) nonzero entries, where p denotes the polynomial degree. The proof of the sparsity requires the assistance of computer algebra software. Several numerical experiments show the efficiency of the proposed bases for higher polynomial degrees p.

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Correspondence to S. Beuchler.

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Beuchler, S., Pillwein, V. Sparse shape functions for tetrahedral p-FEM using integrated Jacobi polynomials. Computing 80, 345–375 (2007). https://doi.org/10.1007/s00607-007-0236-0

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AMS Subject Classifications

  • 65N30
  • 65N35
  • 33C45 (primary)
  • 65N22
  • 65N55
  • 65Q05 (secondary)

Keywords

  • high-order finite elements
  • orthogonal polynomials
  • computer algebra
  • solution of discretized equations