Title

Convergence Analysis of the LDG Method for Singularly Perturbed Two-Point Boundary Value Problems

Document Type

Article

Publication Date

12-1-2011

Department

Mathematics

Abstract

In this paper the local discontinuous Galerkin method (LDG) is considered for solving one-dimensional singularly perturbed two-point boundary value problems of convection-diffusion type and reaction-diffusion type. Error estimates are studied on Shishkin meshes. The L(2) error bounds for the LDG approximation of the solution and its derivative are uniformly valid with respect to the singular perturbation parameter. Numerical experiments indicate that the orders of convergence are sharp.

Publication Title

Communications in Mathematical Sciences

Volume

9

Issue

4

First Page

1013

Last Page

1032