Effect of numerical integration on meshless methods

被引：52

作者：

Babuska, Ivo ^{[2
]}

Banerjee, Uday ^{[1
]}

Osborn, John E. ^{[3
]}

Zhang, Qinghui ^{[4
]}

机构：

[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

[2] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA

[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[4] Sun Yat Sen Univ, Dept Sci Comp & Comp Applicat, Guangzhou 510275, Guangdong, Peoples R China

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2009年 / 198卷 / 37-40期

关键词：

Galerkin methods; Meshless methods; Quadrature; Numerical integration; Error estimates; CONFORMING NODAL INTEGRATION; UNITY QUADRATURE; GALERKIN; PARTITION;

D O I：

10.1016/j.cma.2009.04.008

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we present the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k >= 1. The meshless method was used on a second order Neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of numerical integration. This estimate was obtained under the assumption that the numerical integration scheme satisfied a form of Green's formula. We also indicated how to obtain numerical integration schemes satisfying this property. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2886 / 2897

页数：12

共 50 条

[1] Theoretical analysis of numerical integration in Galerkin meshless methods
Zhang, Qinghui
BIT NUMERICAL MATHEMATICS, 2011, 51 (02) : 459 - 480
[2] Theoretical analysis of numerical integration in Galerkin meshless methods
Qinghui Zhang
BIT Numerical Mathematics, 2011, 51 : 459 - 480
[3] Meshless numerical methods in geomechanics
Modaressi, H
Aubert, P
COMPUTER METHODS AND ADVANCES IN GEOMECHANICS, VOL 1, 1997, : 421 - 426
[4] Numerical solutions of meshless methods
Tao, Wen-Quan
Wu, Xue-Hong
Dai, Yan-Jun
Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering, 2010, 30 (05): : 1 - 10
[5] Multidimensional numerical integration for meshless BEM
Ochiai, Y
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2003, 27 (03) : 241 - 249
[6] Meshless Methods Coupled with Other Numerical Methods
Y. T. GU**
Tsinghua Science and Technology, 2005, (01) : 8 - 15
[7] Numerical integration for three-dimensional meshless BEM
Ochiai, Y
BOUNDARY ELEMENTS XXV, 2003, 18 : 319 - 328
[8] NUMERICAL IMPLEMENTATION OF MESHLESS METHODS FOR BEAM PROBLEMS
Rosca, V. E.
Leitao, V. M. A.
ARCHIVES OF CIVIL ENGINEERING, 2012, 58 (02) : 175 - 184
[9] Numerical integration in Galerkin meshless methods, applied to elliptic Neumann problem with non-constant coefficients
Qinghui Zhang
Uday Banerjee
Advances in Computational Mathematics, 2012, 37 : 453 - 492
[10] Numerical integration in Galerkin meshless methods, applied to elliptic Neumann problem with non-constant coefficients
Zhang, Qinghui
Banerjee, Uday
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2012, 37 (04) : 453 - 492

← 1 2 3 4 5 →