Volume 25, Issue 4
Edge-Oriented Hexagonal Elements
DOI:

J. Comp. Math., 25 (2007), pp. 430-439

Published online: 2007-08

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• Abstract

In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space $Q_1^{(3)}$ and are edge-oriented, analogical to the case of the rotated $Q_1$ quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the $L^2$ norm. This theoretical result is confirmed by the numerical tests.

• Keywords

Nonconforming finite element method Hexagonal element $Q_1$ element

65N15 65N30.

@Article{JCM-25-430, author = {}, title = {Edge-Oriented Hexagonal Elements}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {4}, pages = {430--439}, abstract = { In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space $Q_1^{(3)}$ and are edge-oriented, analogical to the case of the rotated $Q_1$ quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the $L^2$ norm. This theoretical result is confirmed by the numerical tests.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8702.html} }
TY - JOUR T1 - Edge-Oriented Hexagonal Elements JO - Journal of Computational Mathematics VL - 4 SP - 430 EP - 439 PY - 2007 DA - 2007/08 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8702.html KW - Nonconforming finite element method KW - Hexagonal element KW - $Q_1$ element AB - In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space $Q_1^{(3)}$ and are edge-oriented, analogical to the case of the rotated $Q_1$ quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the $L^2$ norm. This theoretical result is confirmed by the numerical tests.