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A Well-Conditioned Hierarchical Basis for Triangular H(curl)-Conforming Elements

Published online by Cambridge University Press:  20 August 2015

Jianguo Xin  and
Wei Cai
Jianguo Xin*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC 28223, USA
Wei Cai*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC 28223, USA
*
Email:[email protected]
Corresponding author.Email:[email protected]
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Abstract

We construct a well-conditioned hierarchical basis for triangular H(curl)-conforming elements with selected orthogonality. The basis functions are grouped into edge and interior functions, and the later is further grouped into normal and bubble functions. In our construction, the trace of the edge shape functions are orthonormal on the associated edge. The interior normal functions, which are perpendicular to an edge, and the bubble functions are both orthonormal among themselves over the reference element. The construction is made possible with classic orthogonal polynomials, viz., Legendre and Jacobi polynomials. For both the mass matrix and the quasi-stiffness matrix, better conditioning of the new basis is shown by a comparison with the basis previously proposed by Ainsworth and Coyle [Comput. Methods. Appl. Mech. Engrg., 190 (2001), 6709-6733].

Keywords

65N3065F3565F15Hierarchical basesH(curl)-conforming elementsmatrix conditioningclassic orthogonal polynomials
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 780 - 806
Copyright
Copyright © Global Science Press Limited 2011

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