TY - JOUR
T1 - A Numerical Study of Uniform Superconvergence of LDG Method for Solving Singularly Perturbed Problems
AU - Ziqing Xie, Zuozheng Zhang & Zhimin Zhang
JO - Journal of Computational Mathematics
VL - 2-3
SP - 280
EP - 298
PY - 2009
DA - 2009/04
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8573.html
KW - Singularly perturbed problems, Local discontinuous Galerkin method, Numerical fluxes, Uniform superconvergence.
AB - <p style="text-align: justify;">In this paper, we consider the local discontinuous Galerkin method (LDG) for solving
singularly perturbed convection-diffusion problems in one- and two-dimensional settings.
The existence and uniqueness of the LDG solutions are verified. Numerical experiments
demonstrate that it seems impossible to obtain uniform superconvergence for
numerical fluxes under uniform meshes. Thanks to the implementation of two-type different
anisotropic meshes, i.e., the Shishkin and an improved grade meshes, the uniform $2p + 1$-order superconvergence is observed numerically for both one-dimensional and two-dimensional
cases.</p>