A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEMS  

作　　者：Ziqing Xie Zuozheng Zhang Zhimin Zhang 

机构地区：[1]Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal University, Changsha 410081, China

出　　处：《Journal of Computational Mathematics》2009年第2期280-298,共19页计算数学（英文）

基　　金：Supported by the National Natural Science Foundation of China (10571053,10871066);the Programme for New Century Excellent Talents in University (NCET-06-0712).

摘　　要：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 ＋ i-order superconvergence is observed numerically for both one-dimensional and twodimensional cases.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 ＋ i-order superconvergence is observed numerically for both one-dimensional and twodimensional cases.

关 键 词：Singularly perturbed problems Local discontinuous Galerkin method Numerical fluxes Uniform superconvergence 

分 类 号：O241.82[理学—计算数学] P456.7[理学—数学]