Camassa-Holm方程的高阶局部中心间断Galerkin有限元法  

High Order Local Central Discontinuous Galerkin-Finite Element Methods for the Camassa-Holm Equation

作　　者：马健军[1] 陈爱敏[2] 郝怡非[1] 

机构地区：[1]四川外国语大学国别经济与国际商务研究中心,重庆400031 [2]重庆大学城市科技学院,重庆402167

出　　处：《四川师范大学学报（自然科学版）》2015年第6期871-874,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：重庆市自然科学基金一般项目(CSTC2012JJA00005)

摘　　要：发展一个求解具有尖波解的Camassa-Holm方程的高阶局部中心间断Galerkin有限元法,该方法首先将Camassa-Holm方程改写为一个守恒律方程和一阶方程组的耦合系统,然后,使用局部中心间断Galerkin法求解该守恒律和使用有限元法求解一阶方程组,数值算例用来检验该方法的精度和有效性.In this paper, we develop high order local central discontinuous Galerkin-finite element methods for solving the Ca- massa-Holm equation which supports peakon solutions. In our numerical approach, we first reformulate the Carnassa-Holm equation into a conservation law coupled with a system of first order equations. Then we propose a family of high order numerical methods which dis- cretize the conservation law with local central discontinuous Galerkin methods and the system of first order equations with continuous fi- nite element methods. Numerical tests are presented to illustrate the accuracy and validity of the proposed schemes.

关 键 词：CAMASSA-HOLM方程 尖波解 局部中心间断Galerkin法 有限元法 

分 类 号：O241.82[理学—计算数学]