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Volume 10, Issue 4
Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh

P. Zhu, Z. Xie & S. Zhou

Int. J. Numer. Anal. Mod., 10 (2013), pp. 845-859.

Published online: 2013-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-845, author = {}, title = {Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/599.html} }
TY - JOUR T1 - Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 845 EP - 859 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/599.html KW - convection diffusion equation, local discontinuous Galerkin method, finite element method, Shishkin mesh, uniform convergence. AB -

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.

P. Zhu, Z. Xie & S. Zhou. (1970). Uniform Convergence of a Coupled Method for Convection-Diffusion Problems in 2-D Shishkin Mesh. International Journal of Numerical Analysis and Modeling. 10 (4). 845-859. doi:
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