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

Authors:
S. Beuchler;J. Schöberl
Affiliations:
Institute f. Computational Mathematics, Johannes-Kepler-University, Altenbergerstrasse 69, 4040, Linz, Austria;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria
Venue:
Numerische Mathematik
Year:
2006

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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.