High-order finite element method on a Bakhvalov-type mesh for a singularly perturbed convection–diffusion problem with two parameters

Abstract

We investigate in this article convergence for a kth(k≥2) order finite element method on a Bakhvalov-type mesh for a two-parameter singularly perturbed two-point boundary value problem. By means of a special interpolation, we obtain the errors for Lagrange interpolation, and then prove the optimal order of convergence. Numerical experiments are given to demonstrate the theoretical results.