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

Authors:
S. Beuchler;V. Pillwein
Affiliations:
JKU Linz, Institute of Computational Mathematics, Altenbergerstr. 69, Linz, Austria;SFB F013, Altenbergerstr. 69, Linz, Austria
Venue:
Computing
Year:
2007

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Abstract

In this paper, we investigate the discretization of an ellipticboundary value problem in 3D by means of the hp-version ofthe finite element method using a mesh of tetrahedrons. We presentseveral bases based on integrated Jacobi polynomials in which theelement stiffness matrix has 𝒪(p3)nonzero entries, where p denotes the polynomial degree. Theproof of the sparsity requires the assistance of computer algebrasoftware. Several numerical experiments show the efficiency of theproposed bases for higher polynomial degrees p.