带间断系数的奇异摄动对流扩散方程的NIPG有限元方法  

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

作　　者：徐磊 刘利斌 Xu Lei;Liu Libin(Center for Applied Mathematics of Guangxi,Nanning Normal University,Nanning 530100)

机构地区：[1]南宁师范大学广西应用数学中心,南宁530100

出　　处：《数学物理学报（A辑）》2024年第6期1499-1510,共12页Acta Mathematica Scientia

基　　金：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)。

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.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.

关 键 词：奇异摄动 间断系数 NIPG 方法 Bakhvalov-type 网格 

分 类 号：O175.23[理学—数学]