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Volume 21, Issue 3
Mathematical Analysis for Quadrilateral Rotated $Q_1$ Element III: The Effect of Numerical Integration

Ping-Bing Ming & Zhong-Ci Shi

J. Comp. Math., 21 (2003), pp. 287-294.

Published online: 2003-06

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  • Abstract

This is the third part of the paper for the rotated $Q_1$ nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a $Q_1$ unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.

  • Keywords

Quadrilateral rotated $Q_1$ element, Numerical quadrature.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-287, author = {Ming , Ping-Bing and Shi , Zhong-Ci}, title = {Mathematical Analysis for Quadrilateral Rotated $Q_1$ Element III: The Effect of Numerical Integration}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {3}, pages = {287--294}, abstract = {

This is the third part of the paper for the rotated $Q_1$ nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a $Q_1$ unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8880.html} }
TY - JOUR T1 - Mathematical Analysis for Quadrilateral Rotated $Q_1$ Element III: The Effect of Numerical Integration AU - Ming , Ping-Bing AU - Shi , Zhong-Ci JO - Journal of Computational Mathematics VL - 3 SP - 287 EP - 294 PY - 2003 DA - 2003/06 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8880.html KW - Quadrilateral rotated $Q_1$ element, Numerical quadrature. AB -

This is the third part of the paper for the rotated $Q_1$ nonconforming element on quadrilateral meshes for general second order elliptic problems. Some optimal numerical formulas are presented and analyzed. The novelty is that it includes a formula with only two sampling points which excludes even a $Q_1$ unisolvent set. It is the optimal numerical integration formula over a quadrilateral mesh with least sampling points up to now.

Ping-Bing Ming & Zhong-Ci Shi. (1970). Mathematical Analysis for Quadrilateral Rotated $Q_1$ Element III: The Effect of Numerical Integration. Journal of Computational Mathematics. 21 (3). 287-294. doi:
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