On the Convergence of the Kriging-based Finite Element Method

An enhancement of the FEM using Kriging interpolation (K-FEM) was recently proposed. This method offers advantages over the conventional FEM and mesh-free methods. With Kriging interpolation, the approximated field over an element is influenced not only by its own element nodes but also by a set of satellite nodes outside the element. This results in incompatibility along interelement boundaries. Consequently, the convergence of the solutions is questionable. In this paper, the convergence is investigated through several numerical tests. It is found that the solutions of the K-FEM with an appropriate range of parameters converge to the corresponding exact solutions.