Numerical integration of the Galerkin weak form in meshfree methods. (English) Zbl 0963.74076

Dolbow, J.; Belytschko, T.

Comput. Mech. 23, No. 3, 219-230 (1999).

From the summary: The numerical integration of Galerkin weak forms for meshfree methods is investigated and some improvements are presented. We review the character of the shape functions in meshfree methods and compare it to those used in the finite element method. 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 method illustrate the effect of these errors on solutions to elliptic problems.

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74S05	Finite element methods applied to problems in solid mechanics
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

quadrature errors; numerical integration; shape functions; subdomains; quadrature cells; meshfree element free Galerkin method