Construction of one-dimensional elements with b-spline wavelet

Adopting the scaling function of BSWI as trial functions, a new finite element method of B-Spline wavelet on the interval (FEM BSWI) is presented. Instead of traditional polynomial interpolation, scaling functions at the certain scale was utilized to form the shape functions and construct wavelet-based elements. Unlike the process of direct wavelets adding in the previous work, the elemental displacement field represented by the coefficients of wavelets expansions was transformed into edges and internal modes via the constructed transformation matrix which serves as the key to constructing elements freely as the non-singularity gets ensured to construct a class of one-dimensional elements. The numerical examples indicate that the BSWI elements have higher efficiency and accuracy in solving problems with variable boundary conditions and structural shapes than the traditional finite element methods.