The finite element method based on interpolating with wavelet basis function

The compactly supported wavelet basis functions are introduced into the con struction of interpolating function of traditional finite element method wh en analyzing the problems with high gradient, and the traditional interpola ting method is modified. The numerical stability of the new interpolating p attern is discussed and the convergence of the new method is also discussed by patch test analysis. The additional freedom of the new interpolating pa ttern is eliminated by static condensation method. Finally, the wavelet fin ite element formulations based on variational principles are put forward.