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

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.