Convergence analysis of the LDG method applied to singularly perturbed problems

Abstract

AbstractConsidering a two‐dimensional singularly perturbed convection–diffusion problem with exponential boundary layers, we analyze the local discontinuous Galerkin (DG) method that uses piecewise bilinear polynomials on Shishkin mesh. A convergence rate O(N‐1 lnN) in a DG‐norm is established under the regularity assumptions, while the total number of mesh points is O(N2). The rate of convergence is uniformly valid with respect to the singular perturbation parameter ε. Numerical experiments indicate that the theoretical error estimate is sharp. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013