Finite element analysis of boundary value problems using wavelet-like basis functions

In this paper the use of wavelet-like basis functions in the finite element analysis of one dimensional problems in which a Dirichlet boundary condition is specified at one boundary and a Neumann boundary condition is specified at the other, is presented. Construction of these types of basis functions for the mixed type boundary conditions is discussed. The condition numbers of the resulting matrices, along with the number of steps required for convergence of the conjugate gradient solution are presented. For comparison, results obtained from a finite element algorithm employing traditional basis functions are also presented.