摘要
通过局部加密网格和提高分片多项式次数两种策略,用hp型间断有限元方法解奇异摄动Volterra积分微分方程.数值计算结果表明,hp型间断有限元解的数值通量在节点处具有与小参数无关的一致指数收敛性,而且hp型间断有限元解在L2范数下具有一致指数收敛性.
By two strategies of locally refined meshes and increasing the degree of piecewise polynomials,the numerical scheme of hp-version discontinuous Galerkin method for singularly perturbed Volterra integro-differential equations is firstly designed in this paper.Then numerical results show that not only the numerical flux of the hp-version discontinuous Galerkin solutions at nodes has the uniform exponential rate of convergence property independent of the singularly perturbed parameter,but also the hp-version discontinuous Galerkin solutions in L2 norm has the uniform exponential rate of convergence property.
作者
陶霞
张映辉
TAO Xia;ZHANG Yinghui(School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,China)
出处
《湖南理工学院学报（自然科学版）》
CAS
2019年第3期1-3,共3页
Journal of Hunan Institute of Science and Technology(Natural Sciences)
基金
国家自然科学基金委数学天元基金资助项目(11426103)
湖南省教育厅优秀青年科学研究项目(16B112)
湖南理工学院教学改革研究项目(2017B16)
湖南省教育科学“十二五”规划青年专项资助课题(XJK015QGD007)
湖南省普通高等学校教学改革研究项目(湘教通[2017]452号-324)
湖南省重点学科建设项目和湖南省高校科技创新团队支持计划项目
关键词
hp型间断有限元方法
奇异摄动Volterra积分微分方程
一致指数收敛
hp-version discontinuous Galerkin method
singularly perturbed Volterra integro-differential equations
uniform exponential rate of convergence
