Research On Application And Error Analysis For Interpolating Element-free Galerkin Method

As interpolating element-free Galerkin method is one of the meshless method, it doesn't need to construct mesh to form the approximation function, just nodal information is enough.Interpolating element-free Galerkin method is constructed by the combination of using the interpolating moving least squares approximation to get the shape function and using Galerkin integral weak form to discrete the differential equation. So its error analysis is based on the error analys is of the interpolating moving least squares method.In the second section, the moving least square method is developed first, then improve it to get the interpolating moving least square method, and their error estimates are discussed. In the third section, potential problems is solved using the interpolating element-free Galerkin method, and its error estimates is discussed. In the forth section, an interpolating element-free Galerkin method for Kd V-B equation is developed and the corresponding formulas are obtained. Related numerical examples are given to varify the effectiveness of method and the correctness of the conclusion in every problem.Because of the interpolating characteristic of the interpolating element-free Galerkin method, its boundary conditions can be applied directly and don't need any other auxiliary method, thus the number of undetermined coefficients is decreased and computational effic iency is improved. The theory of error analys is and numerical results show that the interpolating element-free Galerkin method has high computational accuracy. It is proved that the method is a great numerical method in theoretically, and has many merits, such as high precis ion, high efficiency, wide application, etc.