二维双参数奇异摄动问题的自适应多尺度有限元法探究  

Study on adaptive multiscale finite element method for two-dimensional singularly perturbed problems with two parameters

作　　者：孙美玲[1,2] 陈璐 江山 SUN Meiling;CHEN Lu;JIANG Shan(Department of Mathematics,Nantong Vocational University,Nantong 226007,Jiangsu Province,China;School of Mathematics and Statistics,Nantong University,Nantong 226019,Jiangsu Province,China)

机构地区：[1]南通职业大学数学教研室,江苏南通226007 [2]南通大学数学与统计学院,江苏南通226019

出　　处：《浙江大学学报(理学版)》2025年第3期404-409,共6页Journal of Zhejiang University(Science Edition)

基　　金：国家自然科学基金面上项目(11771224);南通职业大学自然科学研究重点项目(23ZK03)。

摘　　要：研究了二维双参数奇异摄动偏微分方程,因2个跨尺度的小参数可能导致其解跳跃,产生较大误差,故基于双参数的实际跨尺度大小,用迭代算法生成离散化分层网格,提出了自适应多尺度有限元法。该方法在粗网格水平上就能精确高效地逼近跳跃解,有效降低误差,其计算优势和改进效果较传统方法有显著的提升。This paper addresses the two-dimensional singularly perturbed partial differentiable equation with two parameters,since the existence of two scaled small parameters it would bring jumps and large errors of the solution.Based on the values of two scaled parameters,we adopt an iterative algorithm to generate a discrete graded mesh,and propose an adaptive multiscale finite element method on the relative coarse mesh to achieve the accurate and efficient solution,therefore reducing errors reasonably.The new method outperforms traditional methods,and shows evident advantages and updated abilities.

关 键 词：奇异摄动 双参数模型 多尺度有限元法 数值效率 

分 类 号：O241.82[理学—计算数学]