A study of multiscale wavelet-based elements for adaptive finite element analysis

This paper is concerned with the construction of multiscale wavelet-based elements using lifting scheme. In deriving the computational formulation of multiscale elements of B-spline wavelet on the interval (BSWI), the element displacement field represented by the coefficients of wavelets expansion in wavelet space is transformed into the physical degree of freedoms (DOFs) in finite element space via the corresponding transformation matrix. Then 2D C0C0 type multiscale BSWI elements are derived to fulfill the nesting approximation of wavelet finite element method (WFEM). The wavelet-based adaptive algorithm shares the approaches involved in adaptive classical finite element methods. Numerical results indicate that the present multiscale wavelet-based elements are suit for adaptive finite element analysis, especially for singularity problems in engineering. The convergence shown in numerical examples demonstrates the reliability of the elements.