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

Abstract

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 speciped at one boundary and a Neumann boundary condition is specijied at the other, will be presented. Construction of these types of basis functions for the mixed type boundary conditions will be discussed. The condition numbers of the resulting matrices, along with the number of steps required for convergence of the conjugate gradient solution will be presented. For comparison, results obtained @om a finite element algorithm employing traditional basis functions will also be presented.