一类非线性双曲型方程扩展混合有限元方法的误差估计

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 468-478.

一类非线性双曲型方程扩展混合有限元方法的误差估计

王克彦¹,王奇生^2,*()

¹ 衡阳师范学院数学与统计学院湖南衡阳 421008
² 五邑大学数学与计算科学学院广东江门 529020

收稿日期:2020-02-21 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 王奇生 E-mail:282228006@qq.com
基金资助:
湖南省重点实验室项目基金(2016TP1020);衡阳师范学院科学基金(18D12)

Error Estimates for Expanded Mixed Finite Element Methods for Nonlinear Hyperbolic Equation

Keyan Wang¹,Qisheng Wang^2,*()

¹ School of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421008
² School of Mathematics and Computational Science, Wuyi University, Guangdong Jiangmen 529020

Received:2020-02-21 Online:2021-04-26 Published:2021-04-29
Contact: Qisheng Wang E-mail:282228006@qq.com
Supported by:
the Science and Technology Plan Project of Hunan Province(2016TP1020);the Scientific Research Foundation of Hengyang Normal University(18D12)

摘要/Abstract

摘要：

该文针对一类非线性双曲型方程提出了扩展混合有限元方法.首先，建立了半离散扩展混合元格式，获得了半离散扩展混合元解的L^∞（L²）先验误差估计.然后，利用有限差分法对时间项进行离散，建立了全离散扩展混合元格式，并给出了全离散格式下的先验误差估计.最后，通过数值算例验证了理论结果.

关键词: 非线性双曲型方程, 扩展混合有限元方法, 误差估计

Abstract:

In this paper, expanded mixed finite element method is developed for a class of nonlinear hyperbolic equation. A priori error estimate for the space discrete scheme is discussed in L^∞(L²) norm. Centered finite differences are used to advance in time, a fully discrete scheme is proposed. Further, a priori error estimate for the fully discrete scheme is established. Finally, a numerical example is presented to confirm the theoretical results.

Key words: Nonlinear hyperbolic equation, Expanded mixed finite element method, Error estimate

中图分类号:

O241.82

王克彦,王奇生. 一类非线性双曲型方程扩展混合有限元方法的误差估计[J]. 数学物理学报, 2021, 41(2): 468-478.

Keyan Wang,Qisheng Wang. Error Estimates for Expanded Mixed Finite Element Methods for Nonlinear Hyperbolic Equation[J]. Acta mathematica scientia,Series A, 2021, 41(2): 468-478.

图/表 2

参考文献 15

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h	$\\|u-u_h\\|$	Rate	$\\|\mathit{\boldsymbol{ \widetilde{p}} }-\mathit{\boldsymbol{ \widetilde{p}} }_h\\|$	Rate	$\\|\mathit{\boldsymbol{p} }-\mathit{\boldsymbol{ p}} _h\\|$	Rate
1/4	3.0894e-2	-	9.2725e-1	-	9.5987e-1	-
1/8	8.2781e-3	1.90	2.4845e-1	1.90	2.5898e-1	1.89
1/16	2.1875e-3	1.92	6.6111e-2	1.91	6.9392e-2	1.90
1/32	5.8207e-4	1.91	1.7591e-2	1.91	1.8593e-2	1.90
1/64	1.5489e-4	1.91	4.6810e-3	1.91	4.9475e-3	1.91

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