Superconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations

被引：0
作者：
Xiaobin Liu
Dazhi Zhang
Xiong Meng
Boying Wu
机构：
[1] Harbin Institute of Technology,School of Mathematics
[2] Harbin Institute of Technology,School of Mathematics and Institute for Advanced Study in Mathematics
来源：
Science China Mathematics | 2021年 / 64卷
关键词：
local discontinuous Galerkin method; superconvergence; correction function; Radau points; 65M12; 65M60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper investigates superconvergence properties of the local discontinuous Galerkin methods with generalized alternating fluxes for one-dimensional linear convection-diffusion equations. By the technique of constructing some special correction functions, we prove the (2k + 1)-th-order superconvergence for the cell averages, and the numerical traces in the discrete L2 norm. In addition, superconvergence of orders k + 2 and k + 1 is obtained for the error and its derivative at generalized Radau points. All the theoretical findings are confirmed by numerical experiments.
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页码：1305 / 1320
页数：15
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