摘要
构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Petrov-Galerkin方法用于求解微分方程组.该方法具有四阶精度且具有间断Petrov-Galerkin方法的优点.数值实验表明该方法可以达到最优收敛阶而且可以模拟复杂波形相互作用,如孤立子的传播及相互碰撞等.
A local discontinuous Petrov-Galerkin method is proposed for solving three types of partial differential equations with second,third and fourth order derivatives,respectively.They are Burgers type equations,Kd V type equations and bi-harmonic type equations.The method extends discontinuous Petrov-Galerkin method for conservation laws by rewriting corresponding equations into a first order system and solving the system instead of the original equation.The method has a fourth order accuracy and maintains advantages of discontinuous Petrov-Galerkin method.Numerical simulations verify that the method reaches optimal convergence order and simulates well complex wave interaction such as soliton propagation and collision.
作者
赵国忠
蔚喜军
郭虹平
董自明
ZHAO Guozhong;YU Xijun;GUO Hongping;DONG Ziming(Faculty of Mathematics,Baotou Teachers’College,Baotou 014030,China;Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)
出处
《计算物理》
EI
CSCD
北大核心
2019年第5期517-532,共16页
Chinese Journal of Computational Physics
基金
National Natural Science Foundation of China(11761054,11571002,11261035)
Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-15-A07)
Natural Science Foundation of Inner Mongolia Autonomous Region,China(2015MS0108,2012MS0102)
Science Research Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China(NJZZ12198,NJZZ16234,NJZZ16235)