带间断系数的奇异摄动对流扩散方程的 NIPG 有限元方法

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1499-1510.

带间断系数的奇异摄动对流扩散方程的 NIPG 有限元方法

徐磊(),刘利斌^*()

南宁师范大学广西应用数学中心南宁 530100

收稿日期:2023-01-15 修回日期:2024-04-17 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*刘利斌, Email：liulibin969@163.com
作者简介:徐磊, Email：xulei19980919@163.com
基金资助:
国家自然科学基金(12361087);广西科技基地和人才专项(AD23023003);广西研究生教育创新计划资助(YCSW2023438)

Uniformly Convergent NIPG Methods for a Singularly Perturbed Convection-Diffusion Problem with a Discontinuous Convection Coefficient

Xu Lei(),Liu Libin^*()

Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning 530100

Received:2023-01-15 Revised:2024-04-17 Online:2024-12-26 Published:2024-11-22
Supported by:
National Science Foundation of China(12361087);Guangxi Science and Techology Program(AD23023003);Innovation Project of Guangxi Graduate Education(YCSW2023438)

摘要/Abstract

摘要：

针对带间断系数的奇异摄动对流扩散方程, 该文在 Bakhvalov-type 网格下, 构造了一种 NIPG 高阶有限元方法. 基于 Gauß Radau 投影和 Lagrange 插值, 推导出 NIPG 方法的最优一致收敛性.最后的数值实验支持了作者的理论结果.

关键词: 奇异摄动, 间断系数, NIPG 方法, Bakhvalov-type 网格

Abstract:

In this paper, a higher order NIPG method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient is studied. Based on Gauß Radau interpolation and Lagrange interpolation, the convergence of optimal order in an energy norm is derived. Numerical experiments are proposed to confirm our theoretical results.

Key words: Singularly perturbed, Nonsmooth coefficient, NIPG method, Bakhvalov-type mesh

中图分类号:

0175.23

徐磊, 刘利斌. 带间断系数的奇异摄动对流扩散方程的 NIPG 有限元方法[J]. 数学物理学报, 2024, 44(6): 1499-1510.

Xu Lei, Liu Libin. Uniformly Convergent NIPG Methods for a Singularly Perturbed Convection-Diffusion Problem with a Discontinuous Convection Coefficient[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1499-1510.

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