Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem

摘要

A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is discretized on arbitrary nonuniform meshes using first- and second-order difference schemes, including upwind schemes. We give first- and second-order maximum norm a posteriori error estimates that are based on difference derivatives of the numerical solution and hold true uniformly in the small parameter. Numerical experiments support the theoretical results. [References: 31]