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On Higher Order Pyramidal Finite Elements

Published online by Cambridge University Press:  03 June 2015

Liping Liu ,
Kevin B. Davies ,
Michal Křížek  and
Li Guan
Liping Liu*
Affiliation:
Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1, Canada
Kevin B. Davies*
Affiliation:
Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1, Canada
Michal Křížek*
Affiliation:
IInstitute of Mathematics, Academy of Sciences, Žitná 25, CZ-115 67 Prague 1, Czech Republic
Li Guan*
Affiliation:
College of Computer Science, Dongguan University of Technology, Dongguan 523808, Guangdong, China
*
Corresponding author. URL: http://www.math.cas.cz/~krizek Email: liping.liu@lakeheadu.ca
Email: kbdavies@lakeheadu.ca
Email: krizek@math.cas.cz
Email: bgliguan@dgut.edu.cn
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Abstract

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four subtetrahedra that form a given pyramidal element.

Keywords

65N30Pyramidal polynomial basis functionsfinite element methodcomposite elementsthree-dimensional mortar elements
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 2 , April 2011 , pp. 131 - 140
Copyright
Copyright © Global-Science Press 2011

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References

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