Local Error Estimates of the LDG Method for 1-D Singularly Perturbed Problems

Local Error Estimates of the LDG Method for 1-D Singularly Perturbed Problems

Year:    2013

International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 350–373

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2013-IJNAM-572

International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 350–373

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Local discontinuous Galerkin method singularly perturbed local error estimates.