Effect of numerical integration on meshless methods

Ivo Babuška; Uday Banerjee; John E. Osborn; Qinghui Zhang

doi:10.1016/j.cma.2009.04.008

Effect of numerical integration on meshless methods

Ivo Babuška, Uday Banerjee, John E. Osborn, Qinghui Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	2886-2897
Number of pages	12
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	198
Issue number	37-40
DOIs	https://doi.org/10.1016/j.cma.2009.04.008
State	Published - Aug 1 2009

Keywords

Error estimates
Galerkin methods
Meshless methods
Numerical integration
Quadrature

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2009.04.008

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title = "Effect of numerical integration on meshless methods",

abstract = "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.",

keywords = "Error estimates, Galerkin methods, Meshless methods, Numerical integration, Quadrature",

author = "Ivo Babu{\v s}ka and Uday Banerjee and Osborn, {John E.} and Qinghui Zhang",

year = "2009",

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T1 - Effect of numerical integration on meshless methods

AU - Babuška, Ivo

AU - Banerjee, Uday

AU - Osborn, John E.

AU - Zhang, Qinghui

PY - 2009/8/1

Y1 - 2009/8/1

N2 - 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.

AB - 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.

KW - Error estimates

KW - Galerkin methods

KW - Meshless methods

KW - Numerical integration

KW - Quadrature

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DO - 10.1016/j.cma.2009.04.008

M3 - Article

AN - SCOPUS:68049131162

SN - 0045-7825

VL - 198

SP - 2886

EP - 2897

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 37-40

ER -

Effect of numerical integration on meshless methods

Abstract

Keywords

ASJC Scopus subject areas

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