Advertisement

Computational Mechanics

, Volume 23, Issue 3, pp 219–230 | Cite as

Numerical integration of the Galerkin weak form in meshfree methods

  • John Dolbow
  • Ted Belytschko
Article

Abstract

The numerical integration of Galerkin weak forms for meshfree methods is investigated and some improvements are presented. The character of the shape functions in meshfree methods is reviewed and compared to those used in the Finite Element Method (FEM). Emphasis is placed on the relationship between the supports of the shape functions and the subdomains used to integrate the discrete equations. The construction of quadrature cells without regard to the local supports of the shape functions is shown to result in the possibility of considerable integration error. Numerical studies using the meshfree Element Free Galerkin (EFG) method illustrate the effect of these errors on solutions to elliptic problems. A construct for integration cells which reduces quadrature error is presented. The observations and conclusions apply to all Galerkin methods which use meshfree approximations.

Keywords

Finite Element Method Shape Function Galerkin Method Weak Form Elliptic Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • John Dolbow
    • 1
  • Ted Belytschko
    • 1
  1. 1.Departments of Civil and Mechanical Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208

Personalised recommendations