TY - JOUR
T1 - Local Analysis of the Local Discontinuous Galerkin Method with the Generalized Alternating Numerical Flux for Two-Dimensional Singularly Perturbed Problem
AU - Cheng , Yao
AU - Zhang , Qiang
AU - Wang , Haijin
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 785
EP - 810
PY - 2018
DA - 2018/08
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12609.html
KW - Local analysis, local discontinuous Galerkin method, generalized alternating numerical flux, error estimate, singularly perturbed problem.
AB - <p style="text-align: justify;">In this paper, we analyze the local discontinuous Galerkin method with the generalized
alternating numerical flux for two-dimensional singularly perturbed problem with outflow
boundary layers. By virtue of the two-dimensional generalized Gauss-Radau projection and energy
technique with suitable weight function, we obtain the double-optimal error estimate, namely,
the convergence rate in L2-norm out of the outflow boundary layer is optimal, and the width
of boundary layer is quasi-optimal, when piecewise tensor product polynomial space on quasi-uniform
Cartesian meshes are used. Numerical experiments are given to verify the theoretical
results.</p>