Abstract: Wavelet finite element (WFE) method is a new class of finite element approximation method. Wavelet multiresolution analysis theory of signal processing is introduced into finite element analysis, and nesting multiscale finite element ap-proximation spaces are constructed by using wavelet bases as interpolating functions. Thus WFE method can yield an initial coarse description of the solution in lower order approximation space, successively refine the solution in singular regions with adaptive multiresolution. This method has good numerical sta-bility and efficiency to singularity problems. Considering three aspects, wavelet weighted residual method, WFE theory and adaptive WFE, the recent developments of WFE method are reviewed. New progresses of engineering application, such as nonlinear large gradient, quantitative crack prognosis, are in-troduced. Some key techniques, unsolved problems and practi-cal prospect in engineering are indicated.

Key words: Adaptive, Multiresolution, Singularity, Wavelet finite element(WFE)