Error analysis for moving least squares approximation in 2D space

In this paper, we provide a theoretical analysis of the moving least squares (MLS) approximation, which belongs to the family of meshless methods. First the non matrix form of the MLS shape function in two-dimensional space is obtained by using consistency conditions. The error estimates for MLS approximation in Sobolev space are presented when u(x,y)∈Cm+1(Ω)u(x,y)∈Cm+1(Ω), and u(x,y)∈Wm+1,q(Ω)u(x,y)∈Wm+1,q(Ω), respectively. We establish the error estimates for interpolating element-free Galerkin (IEFG) method when it is used for solving Poisson’s equation. The error bound is related to the radii of the weight functions and the bound of the norm of derivatives of shape functions. Three numerical examples are selected to confirm our analysis.