Effect of numerical integration on meshless methods

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.