(untitled) (Journal of Computational Mathematics, 2018)
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|ε |^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.