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.
引用
收藏
页数：9
相关论文
共 50 条
[31]   3D finite element numerical integration on GPUs [J].
Maciol, Pawel ;
Plaszewski, Przemyslaw ;
Banas, Krzysztof .
ICCS 2010 - INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE, PROCEEDINGS, 2010, 1 (01) :1087-1094
[32]   Cascadic multigrid method for isoparametric finite element with numerical integration [J].
Bi, CJ ;
Li, LK .
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2004, 22 (01) :123-136
[33]   Finite element approximation with numerical integration for differential eigenvalue problems [J].
Solov'ev, Sergey I. .
APPLIED NUMERICAL MATHEMATICS, 2015, 93 :206-214
[34]   Numerical Integration on Natural Element Method: Comparative Analyses of Different Approaches [J].
Botelho, Diego Pereira ;
Marechal, Yves ;
Ramdane, Brahim .
2016 IEEE CONFERENCE ON ELECTROMAGNETIC FIELD COMPUTATION (CEFC), 2016,
[35]   Numerical integration algorithms and constraint formulations for an ALE-ANCF cable element [J].
Fotland, Gaute ;
Haugen, Bjorn .
MECHANISM AND MACHINE THEORY, 2022, 170
[36]   On the influence of numerical integration on mixed finite element approximations of a Maxwell eigenvalue problem [J].
Hamelinck, Wouter .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (02) :929-937
[37]   Numerical Integration Strategy for Finite Element Transfer Matrix Method of Nonlinear Dynamics [J].
Qian, Shuang-Lin ;
He, Bin ;
Ge, Wei-Yan ;
Yao, Li-Ke .
INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND COMMUNICATION ENGINEERING (CSCE 2015), 2015, :831-837
[38]   STIFFNESS MATRIX AND THE VECTOR OF NODAL REACTIONS OF CIRCULAR FINITE ELEMENT WITH NUMERICAL INTEGRATION [J].
Guliar, O. ;
Piskunov, S. ;
Shkril', A. ;
Romantsova, K. .
OPIR MATERIALIV I TEORIA SPORUD-STRENGTH OF MATERIALS AND THEORY OF STRUCTURES, 2015, (95) :81-89
[39]   Multi-core and Multiprocessor Implementation of Numerical Integration in Finite Element Method [J].
Mamza, J. ;
Makyla, P. ;
Dziekonski, A. ;
Lamecki, A. ;
Mrozowski, M. .
2012 19th International Conference on Microwave Radar and Wireless Communications (MIKON), Vols 1 and 2, 2012, :457-461
[40]   New Numerical Integration Methods for Simulation of Electromagnetic Transients [J].
Chakraborty, Soham ;
Ramanujam, R. .
INTERNATIONAL JOURNAL OF EMERGING ELECTRIC POWER SYSTEMS, 2018, 19 (04)
12345