Title

Convergence Analysis of the LDG Method Applied to Singularly Perturbed Problems

Document Type

Article

Publication Date

3-1-2013

Department

Mathematics

Abstract

Considering a two-dimensional singularly perturbed convectiondiffusion 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 epsilon. Numerical experiments indicate that the theoretical error estimate is sharp. (C) 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013

Publication Title

Numerical Methods for Partial Differential Equations

Volume

29

Issue

2

First Page

396

Last Page

421