The Theory And Application Of Element-free Galerkin Method With Wavelet Basis

Element-free Galerkin (EFG) method is one of the meshless methods. It has both advantages of the meshless methods and finite element method (FEM) for the mathematical foundation of its governing equation is the same as that of FEM. To take advantage of the excellent localization character of wavelet, cardinal B-splines wavelet basis is used as a substitute for the traditional polynomial basis in this dissertation. Related theories are expatiated first, and then a method is developed for using wavelet in EFG. A series of examples illustrates the excellent performance of the techniques. In addition, two difficulties in EFG, treating essential boundary conditions and approximations near nonconvex boundaries, are discussed. At the end of the dissertation, the potential progresses about coupling wavelet analysis and EFG are discussed.