Uniform pointwise convergence of finite difference schemes for quasilinear convection‐diffusion problems

Abstract

AbstractWe study convergence properties of an upwind difference scheme on layer‐adapted grids for the discretization of a class of singularly perturbed quasilinear two‐point boundary value problems. We derive conditions that are sufficient for uniform convergence in the maximum norm, with respect to the perturbation parameter, of the method. These conditions are easy to check and enable one to immediately deduce the rate of uniform convergence.