%0 Journal Article %1 dolbow-1999-efg-intg %A Dolbow, J. %A Belytschko, T. %D 1999 %J Computational Mechanics %K efg intg mm %N 3 %P 219-230 %T Numerical integration of the Galerkin weak form in meshfree methods %U http://dx.doi.org/10.1007/s004660050403 %V 23 %X 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 integratethe discrete equations. The construction of quadrature cells without regard to the local supports of the shape functions isshown 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 whichreduces quadrature error is presented. The observations and conclusions apply to all Galerkin methods which use meshfree approximations.

@article{dolbow-1999-efg-intg, abstract = {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 integratethe discrete equations. The construction of quadrature cells without regard to the local supports of the shape functions isshown 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 whichreduces quadrature error is presented. The observations and conclusions apply to all Galerkin methods which use meshfree approximations.}, added-at = {2009-08-09T23:02:20.000+0200}, author = {Dolbow, J. and Belytschko, T.}, biburl = {https://www.bibsonomy.org/bibtex/24224fdc3bfa285088528a54ad690726b/pjoyot}, description = {SpringerLink - Article de revue}, interhash = {15ab1e0bb4015f460a7df117e75257de}, intrahash = {4224fdc3bfa285088528a54ad690726b}, journal = {Computational Mechanics}, keywords = {efg intg mm}, month = {#apr#}, number = 3, pages = {219-230}, timestamp = {2009-08-09T23:02:20.000+0200}, title = {Numerical integration of the Galerkin weak form in meshfree methods}, url = {http://dx.doi.org/10.1007/s004660050403}, volume = 23, year = 1999 }