Study On Element-free Galerkin Method Based On The Energy Norm Error

In this paper,the moving least square method is introduced to construct the shape function in the Element-Free Galerkin method.Then,the properties and forms of weight function are introduced,and the influence of radius on numerical results is analyzed.A new method to determine the influence radius of the weight function is constructed by introduced parameters.By comparing the energy norm error under different parameter values,the optimal parameter value is obtained,and the value of the influence radius of the weight function is determined.At the same time,the energy norm errors and CPU consumption time of two kinds of common weight functions under different node distribution and influence radius of different weight functions are analyzed.Secondly,the least square method of moving complex variables is given in combination with the theory of complex variables.Since the functional established in the least square method of moving complex variables has no definite mathematical and physical significance,the improved least square method of moving complex variables is given.Since the shape function constructed in the improved moving least square method of complex variables has no interpolation property,the moving least square interpolation method of complex variables is presented.By combining the moving least square method of complex variables and the moving least square interpolation method of complex variables with the weak form of Galerkin integral of potential problem,the interpolation method of complex variables element-free Galerkin method of potential problem and the interpolation method of complex variables element-free Galerkin method of potential problem are established respectively.The effectiveness of the method are analyzed by numerical examples.