Based on wavelet adaptive finite element analysis

The construction of the second generation wavelet based on the lifting scheme and the framework for solving partial differential equation method is presented in this paper. This paper also gives a multiresolution finite element method. Finally, based on the second generation wavelet, a multiresolution finite element method is presented, and the corresponding adaptive algorithm is constructed. The hierarchical approximation spaces for finite element analysis are produced and the decoupling condition of the stiffness matrix of the finite element equation is established by introducing wavelet vanishing moments. A class of second generation wavelet-based beam elements is constructed by using second generation wavelet function.