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 -

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.