高阶偏微分方程局部间断Galerkin方法的最优误差估计（英文）  

Optimal Error Estimates of the Local Discontinuous Galerkin Method for the High Order Partial Differential Equations

作　　者：金宇秋 杜若 李迎庆 程瑶 JIN Yuqiu;DU Ruo;LI Yingqing;CHENG Yao(School of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou,Jiangsu,215009,P.R.China)

机构地区：[1]苏州科技大学数理学院,苏州江苏215009

出　　处：《数学进展》2019年第2期241-256,共16页Advances in Mathematics（China）

基　　金：supported by Natural Science Foundation of Jiangsu Province(No.BK20170374);Nature Science Research Program for Colleges and Universities of Jiangsu Province(No.17KJB110016);Scientific Research Project for University Students of Suzhou University of Science and Technology in 2017-2018

摘　　要：本文针对含三阶和四阶空间导数的高阶偏微分方程,得到了基于广义交替数值通量局部间断Galerkin方法的最优L^2-模误差估计.主要技术是基于有关辅助变量的能量方程和最新提出的整体Gauss-Radau投影.数值实验验证了理论结果.We study the local discontinuous Galerkin(LDG) method based on the generalized alternating numerical fluxes for the high order partial differential equation containing the third order or fourth order spatial derivative terms. Optimal L^2-norm error estimates are obtained for the corresponding semi-discrete LDG method. The main technique is to derive the energy equation for various auxiliary variables and to use the newly developed generalized Gauss-Radau projection. Numerical experiments are given to verify the sharpness of the theoretical results.

关 键 词：高阶方程 LDG方法 数值通量 广义Gauss-Radau投影 误差估计 

分 类 号：O241.1[理学—计算数学]