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.