As a new numerical method, free element method has the advantages of both finite element method and meshless method. The main feature of the method is that only one independent element formed by freely selecting surrounding points is required for each collocation point, without need to consider the connective relationship between adjacent elements and the continuity of physical variables and their spatial derivatives at interfaces of the connected elements. In this paper, based on the free element method, the weak form integral expression of the governing equation is established by using the weighted residual method, and the influence of different weight functions on the calculation accuracy is discussed.This method used Lagrangian interpolation in the interpolation of free cells. By changing the integration area and the weight function, different integration expressions can be obtained, so as to analyze the calculation accuracy under different weak forms.