Study of wavelet finite element method and its engineering application.

A new finite element space is studied, in which the scaling functions of Daubechies wavelets are considered as the interpolation basis functions, and then the wavelet finite element (WFE) is constructed. In order to overcome the integral difficulty for lack of explicit scaling function expression, a new and efficient integral method for stiffness matrix and load matrix is presented by employing two-scale equations. The bending for a thin plate equations based on WFE is derived, and the bending characters of thin plate and the inner temperature distribution of office paper are studied. Numerical results indicate that WFE has desirable calculation precision and can eliminate 0.5% numerical distortion caused by temperature changes. WFE is superior to traditional finite element method while dealing with large gradient problem, such as suddenly changing boundary condition.