A second-order three-point difference scheme on a posteriori mesh for a singularly perturbed convection–diffusion problem

Abstract

In this paper a three-point difference scheme based on a posteriori mesh is used to solve a second-order singularly perturbed convection–diffusion problem. A hybrid difference method is constructed on an arbitrary mesh. A posteriori error analysis is developed for the three-point difference scheme on an arbitrary mesh. A solution-adaptive algorithm based on a posteriori error estimation is devised by equidistributing a monitor function. Numerical experiments illustrate that the scheme is second-order uniformly convergent.