Title

LOCAL ERROR ESTIMATES OF THE LDG METHOD FOR 1-D SINGULARLY PERTURBED PROBLEMS

Document Type

Article

Publication Date

2013

Department

Marine Science

Abstract

In this paper local discontinuous Galerkin method (LDG) was analyzed for solving 1-D convection-diffusion equations with a boundary layer near the outflow boundary. Local error estimates are established on quasi-uniform meshes with maximum mesh size h. On a subdomain with O (h ln(1/h)) distance away from the outflow boundary, the L-2 error of the approximations to the solution and its derivative converges at the optimal rate O (h(k+1)) when polynomials of degree at most k are used. Numerical experiments illustrate that the rate of convergence is uniformly valid and sharp. The numerical comparison of the LDG method and the streamline-diffusion finite element method are also presented.

Publication Title

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING

Volume

10

Issue

2

First Page

350

Last Page

373

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