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

• Published in: Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 49; no. 5; pp. 564 - 569
• Main Authors: Sun, Meiling, Jiang, Shan
• Format: Journal Article
• Language: Chinese
• Published: Hangzhou Zhejiang University 01.09.2022; Zhejiang University Press
• Subjects: Basis functions; Convection-diffusion equation; Diffusion layers; Finite element method; Parameters; Twin boundaries; Two dimensional boundary layer; 一致稳定; 两端边界层; 多尺度有限元; 奇异摄动; 自适应网格
• ISSN: 1008-9497
• DOI: 10.3785/j.issn.1008-9497.2022.05.007

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.