Effect of numerical integration on a new rotated nonconforming quadrilateral element

被引：0
作者：
Meng, Zhaoliang [1 ,2 ]
Cui, Jintao [4 ,5 ]
Luo, Zhongxuan [1 ,3 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
[2] Key Lab Computat Math & Data Intelligence Liaonin, Dalian 116024, Peoples R China
[3] Dalian Univ Technol, Sch Software, Dalian 116620, Peoples R China
[4] Jinan Univ, Dept Math, Guangzhou 510632, Peoples R China
[5] Hong Kong Polytech Univ, Dept Appl Math, Hung Hum, Hong Kong, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 402卷
关键词：
Nonconforming element; Nonparametric; Numerical integration; Quadrilateral mesh; Q(1) ELEMENT; 4-NODE;
D O I：
10.1016/j.cam.2021.113798
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new nonparametric nonconforming quadrilateral finite element is used to approximate the general second-order elliptic problem in two dimensions. Some optimal numerical integration formulas are presented and analyzed. These formulas are derived on a reference quadrilateral which can be linearly mapped to a physical quadrilateral. The novelty of these formulas is that they only involve two quadrature nodes which excludes even a Q(1) unisolvent set, and they are not required to be exact for all the shape functions. Numerical tests show that the presented quadrature rules can also be used coupled with other low-order elements. (C) 2021 Elsevier B.V. All rights reserved.
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页数：9
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