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New shape functions for triangular p-FEM using integrated Jacobi polynomials

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Abstract

In this paper, the second order boundary value problem −∇·((x,y)∇u)=f is discretized by the Finite Element Method using piecewise polynomial functions of degree p on a triangular mesh. On the reference element, we define integrated Jacobi polynomials as interior ansatz functions. If is a constant function on each triangle and each triangle has straight edges, we prove that the element stiffness matrix has not more than nonzero matrix entries. An application for preconditioning is given. Numerical examples show the advantages of the proposed basis.

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Authors and Affiliations

  1. Institute f. Computational Mathematics, Johannes-Kepler-University, Altenbergerstrasse 69, 4040, Linz, Austria

    S. Beuchler

  2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria

    J. Schöberl

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  1. S. Beuchler
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  2. J. Schöberl
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Beuchler, S., Schöberl, J. New shape functions for triangular p-FEM using integrated Jacobi polynomials. Numer. Math. 103, 339–366 (2006). https://doi.org/10.1007/s00211-006-0681-2

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