A robust adaptive method for singularly perturbed convection–diffusion problem with two small parameters

Numerical treatment for a one dimensional two-parameter singularly perturbed convection–diffusion equation is proposed and analyzed. The upwind finite difference method is applied to the problem. Maximum-norm a posteriori error estimates are obtained and used to establish an adaptive algorithm. The uniform convergence of the new algorithm is proved under feasible conditions of two parameters. Numerical experiments are given to confirm the analytical results.