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 - <p style="text-align: justify;">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>