Nodal superconvergence of the local discontinuous Galerkin method for singularly perturbed problems

In this paper, a superconvergence of order (lnN∕N)2k+1 for the numerical traces of the LDG approximation to a one dimensional singularly perturbed convection-diffusion-reaction problem is proved. The LDG method is applied on a Shishkin mesh with 2N elements, and we use polynomials of degree at most k on each element. This result puts the numerical finding reported in Xie and Zhang (2007), Xie et al. (2009) on firm mathematical ground.