Optimal pointwise convergence of the LDG method for singularly perturbed convection–diffusion problem

Abstract

A local discontinuous Galerkin (LDG) method is considered for a one-dimensional singularly perturbed convection–diffusion problem with an exponential boundary layer. Based on the technique of discrete Green’s function, we establish optimal pointwise convergence (up to a logarithmic factor) of the LDG method on three typical families of layer-adapted meshes: Shishkin-type, Bakhvalov–Shishkin-type and Bakhvalov-type. Numerical experiments are also given.