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

[21] Numerical integration of singularities in meshless implementation of local boundary integral equations
V. Sladek
J. Sladek
S. N. Atluri
R. Van Keer
Computational Mechanics, 2000, 25 : 394 - 403
[22] A comparison of numerical integration rules for the meshless local Petrov–Galerkin method
Annamaria Mazzia
Massimiliano Ferronato
Giorgio Pini
Giuseppe Gambolati
Numerical Algorithms, 2007, 45 : 61 - 74
[23] Accurate numerical integration in 3D meshless peridynamic models
Galvanetto, U.
Scabbia, F.
Zaccariotto, M.
CURRENT PERSPECTIVES AND NEW DIRECTIONS IN MECHANICS, MODELLING AND DESIGN OF STRUCTURAL SYSTEMS, 2022, : 161 - 162
[24] Numerical solution of compartmental models by meshless and finite difference methods
Siraj-ul-islam
Haider, Nadeem
APPLIED MATHEMATICS AND COMPUTATION, 2014, 238 : 408 - 435
[25] THE NON-LINEAR NUMERICAL ANALYSIS USING MESHLESS METHODS
Belinha, Jorge
Dinis, Lucia
Jorge, Renato N.
M2D2015: PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON MECHANICS AND MATERIALS IN DESIGN, 2015, : 2309 - 2310
[26] Methods for enhancing numerical integration
de Doncker, E
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT, 2003, 502 (2-3): : 358 - 363
[27] MESHLESS METHODS
Mosova, Vratislava
APLIMAT 2005 - 4TH INTERNATIONAL CONFERENCE, PT II, 2005, : 235 - 239
[28] The effect of numerical integration in finite element methods for nonlinear parabolic equations
Germain N.
Applied Mathematics-A Journal of Chinese Universities, 2001, 16 (2) : 219 - 230
[29] THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS
N’guimbi GermainDept.ofMath.
AppliedMathematics:AJournalofChineseUniversities, 2001, (02) : 219 - 230
[30] THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR SOBOLEV EQUATIONS
N’guimbi Germain (Department of Mathematics
NumericalMathematicsAJournalofChineseUniversities(EnglishSeries), 2000, (02) : 222 - 233

← 1 2 3 4 5 →