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.