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Volume 3, Issue 2
On Higher Order Pyramidal Finite Elements

Liping Liu, Kevin B. Davies, Michal Křížek & Guan Li

Adv. Appl. Math. Mech., 3 (2011), pp. 131-140.

Published online: 2011-03

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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 sub-tetrahedra that form a given pyramidal element.

  • Keywords

Pyramidal polynomial basis functions, finite element method, composite elements, three-dimensional mortar elements.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-131, author = {Liu , LipingDavies , Kevin B.Křížek , Michal and Li , Guan}, title = {On Higher Order Pyramidal Finite Elements}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {2}, pages = {131--140}, 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 sub-tetrahedra that form a given pyramidal element.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0989}, url = {http://global-sci.org/intro/article_detail/aamm/161.html} }
TY - JOUR T1 - On Higher Order Pyramidal Finite Elements AU - Liu , Liping AU - Davies , Kevin B. AU - Křížek , Michal AU - Li , Guan JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 131 EP - 140 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.09-m0989 UR - https://global-sci.org/intro/article_detail/aamm/161.html KW - Pyramidal polynomial basis functions, finite element method, composite elements, three-dimensional mortar elements. AB -

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 sub-tetrahedra that form a given pyramidal element.

Liping Liu, Kevin B. Davies, Michal Křížek & Li Guan. (1970). On Higher Order Pyramidal Finite Elements. Advances in Applied Mathematics and Mechanics. 3 (2). 131-140. doi:10.4208/aamm.09-m0989
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