多尺度有限元法结合分层网格模拟二维奇异摄动的两端边界层问题  

Simulation of multiscale finite element method on graded meshes for two-dimensional singularly perturbed twin boundary layers problems

作　　者：孙美玲[1,2] 江山 SUN Meiling;JIANG Shan(Department of Mathematics,Nantong Vocational University,Nantong 226007,Jiangsu Province,China;School of Science,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]南通大学理学院,江苏南通226019

出　　处：《浙江大学学报（理学版）》2022年第5期564-569,共6页Journal of Zhejiang University（Science Edition）

基　　金：南通市基础科学研究指令性项目(JC2021123);国家自然科学基金面上项目(11771224);江苏省高校青蓝工程优秀骨干教师资助项目。

摘　　要：通过摄动系数建立分层网格,用多尺度有限元法捕捉对流扩散方程的两端边界层,研究二维奇异摄动模型。基于分层网格并利用多尺度基函数刻画了边界层的微观信息,用有限的计算资源、较短的计算时间,得到了不依赖于摄动系数、一致稳定的模拟结果。To solve a two-dimensional singularly perturbed model, a multiscale finite element method on graded meshes built from the perturbed parameter is presented for capturing the twin boundary layers of convection-diffusion equations effectively. Based on the graded meshes, the multiscale basis functions are capable of subtly describing the microscopic information in the boundary layers. No wonder, it just costs a handful of computing resource and short time to achieve the accurate and efficient results, and the results are independent of the perturbed parameter with uniform stability.

关 键 词：奇异摄动 自适应网格 两端边界层 多尺度有限元 一致稳定 

分 类 号：O241.82[理学—计算数学]