@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} }