Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh

Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh

Year:    2013

International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 845–859

Abstract

In this paper, we introduce a coupled approach of local discontinuous Galerkin (LDG) and continuous finite element method (CFEM) for solving singularly perturbed convection-diffusion problems. When the coupled continuous-discontinuous linear FEM is used under the Shishkin mesh, a uniform convergence rate $O(N^{-1}ln N)$ in an associated norm is established, where $N$ is the number of elements. Numerical experiments complement the theoretical results. Moreover, a uniform convergence rate $O(N^{-2})$ in $L^2$ norm, is observed numerically on the Shishkin mesh.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2013-IJNAM-599

International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 845–859

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    convection diffusion equation local discontinuous Galerkin method finite element method Shishkin mesh uniform convergence.