Least-squares collocation meshless method

A 1nite point method, least-squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satis1ed not only at the collocation points but also at the auxiliary points in a least-squares sense. The moving least-squares interpolant is used to construct the trial functions. The computational e;ort required for the present method is in the same order as that required for the direct collocation, while the present method improves the accuracy of solution signi1cantly. The proposed method does not require any mesh so that it is a truly meshless method. Three numerical examples are studied in detail, which show that the proposed method possesses high accuracy with low computational e;ort