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Numerische Mathematik

, Volume 103, Issue 3, pp 339–366 | Cite as

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

  • S. Beuchler
  • J. Schöberl
Article

Abstract

In this paper, the second order boundary value problem −∇·( Open image in new window (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 Open image in new window is a constant function on each triangle and each triangle has straight edges, we prove that the element stiffness matrix has not more than Open image in new window nonzero matrix entries. An application for preconditioning is given. Numerical examples show the advantages of the proposed basis.

Keywords

Mathematical Method Shape Function Jacobi Polynomial 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Institute f. Computational MathematicsJohannes-Kepler-UniversityLinzAustria
  2. 2.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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