反应扩散问题的新的绝对稳定hp间断Galerkin方法

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 385-394.

反应扩散问题的新的绝对稳定hp间断Galerkin方法

葛志昊¹, 曹济伟²

1. 河南大学应用数学研究所 & 数学与统计学院河南开封 475004;
2. 河南财经政法大学数学与信息科学学院郑州 450000

收稿日期:2016-12-22 修回日期:2017-09-01 出版日期:2018-04-26 发布日期:2018-04-26
通讯作者: 葛志昊 E-mail:10100084@vip.henu.edu.cn
作者简介:曹济伟,E-mail:caojiwei@huel.edu.cn
基金资助:
河南省自然科学基金（162300410031）和河南省基本科研业务费优秀青年培养计划（yqpy20140039）

A New Absolutely Stable hp Discontinuous Galerkin Methodfor the Reaction-Diffusion Problem

Ge Zhihao¹, Cao Jiwei²

1. Institute of Applied Mathematics & School of Mathematics and Statistics, Henan University, Henan Kaifeng 475004;
2. College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450000

Received:2016-12-22 Revised:2017-09-01 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the Natural Science Foundation of Henan Province (162300410031), and the Excellent Youth Program of the Basic Research Operating Expenses Program of Henan Province (yqpy20140039)

摘要/Abstract

摘要： 针对一类反应扩散问题提出了新的绝对稳定hp间断Galerkin方法，并给出了该方法的误差估计，证明了该方法在L²范数和H¹范数意义下是最优阶收敛.最后，数值算例验证了理论结果的正确性.

关键词: 反应扩散问题, 间断Galerkin方法, 最优误差估计

Abstract: In this paper, a new absolutely stable hp discontinuous Galerkin method is proposed. And the error estimate of hp discontinuous Galerkin method is given, and the optimal convergent orders in L²-norm and H¹-norm for the general stabilization parameters are proved. Finally, the numerical tests verify the theoretical results.

Key words: Reaction-diffusion problem, Discontinuous Galerkin method, Optimal error estimation

中图分类号:

O241.82

葛志昊, 曹济伟. 反应扩散问题的新的绝对稳定hp间断Galerkin方法[J]. 数学物理学报, 2018, 38(2): 385-394.

Ge Zhihao, Cao Jiwei. A New Absolutely Stable hp Discontinuous Galerkin Methodfor the Reaction-Diffusion Problem[J]. Acta mathematica scientia,Series A, 2018, 38(2): 385-394.

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