Communications in Mathematical Sciences

Volume 9 (2011)

Number 4

Convergence analysis of the LDG method for singularly perturbed two-point boundary value problems

Pages: 1013 – 1032

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n4.a4

Authors

Haiyan Tian (Department of Mathematics, University of Southern Mississippi)

Zhimin Zhang (Department of Mathematics, Wayne State University, Detroit, Michigan)

Huiqing Zhu (Department of Mathematics, University of Southern Mississippi)

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 L² 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.

Keywords

local discontinuous Galerkin method, singularly perturbed, Shishkin mesh

2010 Mathematics Subject Classification

65L11, 65N15, 65N30

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