DISSIPATIVE NUMERICAL METHODS FOR THE HUNTER-SAXTON EQUATION

作     者：Yan Xu Chi-Wang Shu 

作者机构：Department of Mathematics University of Science and Technology of China Hefei 230026 China Division of Applied Mathematics Brown University Providence RI 02912 USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2010年第28卷第5期

页      面：606-620页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by NSFC grant 10601055 FANEDD of CAS and SRF for ROCS SEM supported by NSF grant DMS-0809086 ARO grant W911NF-08-1-0520 

主　　题：Discontinuous Galerkin method Local discontinuous Galerkin method dissi-pation Hunter-Saxton equation Stability. 

摘      要：In this paper, we present further development of the local discontinuous Galerkin （LDG） method designed in [21] and a new dissipative discontinuous Galerkin （DG） method for the HuntermSaxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].