ERROR ESTIMATES OF THE FINITE ELEMENT METHOD WITH WEIGHTED BASIS FUNCTIONS FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATION

In this paper, we establish a convergence theory for a finite element method with weighted basis functions for solving singularly perturbed convection-diffusion equations. The stability of this finite element method is proved and an upper bound O（h｜lnε｜3/2） for errors in the approximate solutions in the energy norm is obtained on the triangular Bakhvalov-type mesh. Numerical results are presented to verify the stability and the convergent rate of this finite element method.